@Crash, Could the current custodian of that 403(b) perform the initial rollover to an IRA? Whatever it’s now invested in would remain the same for that purpose. Once you’ve moved that money into a traditional IRA you should be able to perform IRA transfers to whatever custodian(s) you want. The IRAs can later easily be converted to Roths all together or in chunks.
That’s what I did with my 403(b) - which was already with TRP. Price was most helpful in facilitating that rollover. The funds I was invested in stayed the same. No money moved. Just a bit of paperwork. Later, I diversified away from Price into some other houses by doing simple IRA Transfers. Paperwork for an IRA transfer takes less than 15 minutes. Pretty basic. Just mail it in.
Changing from a 403(b) designation to IRA status would seem the important first step. Later, deciding which portions of the IRA to convert to Roths and how to time those conversions requires more foresight and planning on your part. The whole chunk doesn’t have to be converted at once. I found it simplest and most convenient to convert 100% of my holdings at different houses in 3 different years. It also allows you to pick the most opportune investments to convert at different times.
PS - In a 403 plan the employer controls it. In an IRA you have control. Big difference.
Just some ideas FWIW

Thanks, everyone. Wife will not have worked at all for pay between Oct 11th and December 31st, 2019. I'm not working at all, taking SS and pension. I'm 65, she's 46. My reference to "not making enough money from which to deduct contributions into Trad. IRA" is a throwback to my own situation a couple/few years ago. We file jointly. There have been 3 years, lately, when my Trad-IRA contributions were non-deductible. (So, I've stopped putting any money into it.) Not because we maxed-out to the IRS-declared legal deductible limit and went beyond it, but because there was not enough income to be TAXED. And late in 2019, we moved from Massachusetts to Hawaii.)
(My tax guy explained the procedure and percentages and steps and nonsense and crapola and bullshit re: exactly what kind of mathematical formula the IRS uses to let me get at that $7,000 total in non-deductible (and zero tax owed) contributions. Clearly, some Martian with 8 brain cells and both male and female genitalia and no experience at all on planet Earth came up with that idiotic gobbledigook.... Now that I'm of age, I COULD take out the non-taxable amount without penalty. But it can't be done simply by taking the $7,000.00, since that's the non-taxable total amount in the account. The IRS requires that it be done over time, in order to preserve the tax-free status of that full amount. M-I-C... K-E-Y....... M-O-U-S-E.)
So, I'm hearing great things from you all about the Roth.
Is it not possible to convert the 403b DIRECTLY and TOTALLY into a Roth? Maybe that IS possible, but for some arcane reason, should not be done? Because the conversion (of whatever amount) triggers a taxable event?
Note: together, we will be WAY below the 12% tax bracket's income limit. PLENTY of room, there. BUT: maybe converting the 403b entirely in a single year might be the difference between owing no tax at all, and owing SOME tax.
I'm re-reading my entry, here. I'm going to just finish here. I'm only going to add this, which is the same thing I've volunteered to say to some customer rage and aggravation agents (aka "customer service") on the phone, just today, in fact: NOTHING should be THIS complicated. :)

As far as I can tell the only share classes still open to new retail incur either a front or back-end load (which may be waived at certain brokerages) and well above average expenses. It's a good fund, make no mistake. But for those at T Rowe Price their own PRGSX is an excellent alternative and performance has been practically identical to PRJZX over the last 7 years with slightly better risk management.

Thanks for the input john. The new muni fund would be a small part of my portfolio. I have a large CG from AKREX in my taxable account that I plan to capture next year and buy the muni fund with that CG. I have set up my retirement to use saved cash to supplement my SS for a couple of years. I plan to be in the 0% tax bracket. This muni fund may be used to extend the cash allowing me to do some Roth conversions.

I'm not clear on the income/tax situation: "If she doesn't make enough money from which to deduct IRA contributions."
So let's start with the mechanics. First, as @Gary1952 said, don't take a taxable distribution. If you're going to pay taxes, you're better off rolling it into a Roth. All its future earnings will be tax free, as opposed to taxable in a taxable account.
The law allows rollover conversions directly from a 403(b) into a Roth IRA. This eliminates one step in the conversion process. But my limited experience in helping someone do this within TIAA suggests that the 403(b) administrators may not know what they're doing. (In that case, TIAA withheld state income taxes which they were not supposed to do.)
Instead, a direct rollover to a T-IRA will preserve your options to convert or not. If you should convert the IRA (or a portion) to a Roth, don't have taxes withheld, else the amount withheld will be treated as a taxable withdrawal. In addition, the conversion moneycannot be withdrawn penalty free for five years. Because your wife is (and will continue to be) under 59½ the conversion money will be subject to the usual 10% early withdrawal tax until it becomes a qualified distribution. That happens five years after the conversion.
Here's a short column discussing these two "traps":
https://www.irahelp.com/slottreport/roth-ira-conversion-10-penalty-trap
In some states (I don't remember which state you're in), some retirement distributions (including IRA withdrawals/conversions, pension plans, etc.) can be taken state-tax-free. This feature may be age-restricted. For example, Colorado exempts $20K of retirement income (including IRA withdrawals) for people aged 55-64, and $24K for seniors. So if you're thinking about converting the money, it might make more sense for you to convert part of your T-IRA (if any) rather than part of your wife's. Not to mention that you're closer to RMDs.
Page with table of how each state treats retirement income:
https://taxna.wolterskluwer.com/whole-ball-of-tax-2018/state-retirement-taxes
That gets us to whether it even makes sense to convert (which is effectively what you're doing if you do a direct rollover to a Roth). Not enough information to reasonably comment here, especially since I don't understand what you mean by "doesn't make enough money". Generally 100% of compensation can be contributed to T-IRAs (up to contribution limits, of course).
The 12% bracket that @bee mentioned calls to mind another consideration: 0% capital gains. If you keep your total taxable income under $78,750 (sic), then you cap gains are taxed at 0% by the IRS. Note that this limit is slightly different from the $78, 950 limit for the 12% ordinary income tax bracket (MFJ).
Too many considerations and too little information to comment intelligently about your conversion decision (which would be informational in any case and not constitute advice, as with all of this post).

Not too surprised by the performance on this one if you look at its collective PE and the top holdings. One heck of a run for growth stocks these past 10 years.

IMHO the Roth is the greatest thing since sliced bread (or cheese). For me, financially speaking, it’s “the gift that keeps on giving.” Great tips from @bee regarding tax-wise planning (an area I’m deficient in). Don’t overlook the benefit that, unlike traditional IRAs, the Roth is (normally) exempt from RMD requirements. As an “oldster” I appreciate that added flexibility.
Ideally, as with any kind of investment option, you like to “buy” low. While most any time is a pretty good time to convert (Traditional to Roth), if you can do it with under-appreciated (or underwater) assets, you stand to reap a larger measure of the Roth’s rewards. That in turn makes that initial tax hit look a lot less. Of course, this is to a degree based on good luck.
I did a conversion of global equity funds in March ‘09 and have never looked back. All smiles. Did another in January 2016 when most of the hype over PRPFX had faded and the fund had slid into disrepute. The hot money had left. Recent performance stunk. Caught a nice bounce with that one. No regrets. No sweat.
The third one (actually the second in sequence) in January, 2015 did not go as planned. I threw all of that conversion into a commodities fund at Oppenheimer I thought was ready for a bounce. Instead it tumbled further. Adding insult to injury, they shut the fund down while all my Roth money was still in it. At one point my “hypothetical” 10K Roth “investment“ was worth in the vicinity of 7K. Never despair. With a bit of help from Invesco/Oppenheimer’s precious metals and real estate funds, that “hypothetical” 10K Roth is now worth over $13,000 - less than 5 years after the conversion.
So, 2 out of 3 ain’t bad. And, even the one “miss” eventually turned around in time to salvage the converted amount.

As a new retiree I sure wish I had more in my Roth. The last 2 years of work I had a Roth option in the 401k and put as much as possible. Having said that I would try to get the Roth funded. I believe you will have to roll it into the equivalent IRA as the 403b. But you can convert in low tax years into Roth from TIRA. Future IRA contributions are a different matter than rolling over.
Do not redeem into taxable.

I have been using a % in HY Munis for years in one of the following funds NHMAX, OPTAX, ORNAX, PHMIX based on momentum.

This is a very well written article. Discusses the pros and cons of the energy market. It’s curious that the article is dated December 24. Oil (the commodity) has been moving higher for at least a month. Brent is leading NYMEX and topped-out at around $68 today. Was under $50 early in the year.
The refiners should have followed oil higher. The closest thing I own (to refiners) is PRNEX. It’s a natural resources fund, but traditionally keeps a heavy footprint in energy. Here’s the top holdings (from Morningstar):
Total SA
Linde PLC
Bp Plc, London
Air Products & Chemicals Inc
NextEra Energy Inc
TC Energy Corp
EOG Resources Inc
Concho Resources Inc
ConocoPhillips
RPM International Inc
With today’s .32% gain, PRNEX is now up close to 17% YTD. Most years that would be considered a nice return. However, with 30% & 40% gains in some other sectors, a mere 17% this year receives little respect.

@stillers - I pulled this off Fidelity's Fixed Income research site:
"Municipal bond volume will finish the year above $400 billion for the fourth time since 2010 and third time in the past four years.
“Considering how slow the year started, no one had that number or thought we would get there,” said one New York trader. “We were one pace for only about $330 billion six months in and then boom, all of a sudden all the taxables hit and here we are.”
The muni market saw $433.27 billion back in 2010, $444.79 billion in 2016, and a record high $448.61 billion in 2017.
“Expectations are high for next year volume wise,” he said. “Buyers should still be eager to buy munis as a true taxes safe haven, with principal, interest and callable bonds that should amplify demand as well. Munis are poised for another big year."
There are no deals on the calendar until the week of Jan. 6. The New York MTA is scheduled to sell $1.5 billion in two separate competitive sales on Monday, Jan. 6. They are then scheduled to jump back into the market on Thursday, Jan. 9 when the authority is expected to sell a total of $939.555 million of green bonds in three separate sales."

https://www.bondbuyer.com/news/municipals-poised-for-big-year-in-2020?position=editorial_1&campaignname=BB_Daily_DailyBriefing_Test_NonPaid-12262019&utm_source=newsletter&utm_medium=email&utm_campaign=BB_Daily_DailyBriefing_Test_NonPaid+'-'+12262019&bt_ee=6xDRiBdbmXsKTnOsUFN43QBpoDTPTVYDzFJZMshHtNhVeVAi1WqYbBH6KClbYWoE&bt_ts=1577358077086
Munis poised for big year in 2020
By Aaron Weitzman
Munis finished above $400 billion for the fourth time since 2010 and fourth time in the past three years.

FD: "Why would any reasonable retiree go for a long term of 3% performance for their whole taxable account?"
FD, my statement above was: "I have generally wanted funds in my taxable account, with an average total return history of over 3%." Some funds in my taxable account have a total return history (at least 5 years) of close to 5%, some have a total return history of close to 4%, and some have a total return history of a little over 3%. BTMIX and DBLSX had a 2019 performance of over 3% (the only year I owned them, but there longer term history is not as good as other funds in my taxable account, and I am not counting on them to exceed a TR of over 3% going forward, so I am considering replacing them.
Secondly, I would request that you not engage in criticizing, or questioning, any poster on this thread, including me. Each investor has their own personal reasons for why they hold certain bond oefs, and it is not my place to tell anyone they are doing anything wrong, or that they are somehow not a good investor because they pick funds different than I pick. I would like to request you follow that principle in your commentary on this thread, and cease being critical of what others are doing. I

dtconroe: I have held BTMIX for all of 2019, and it had a good year, but it averages below 3% total return over its history. I have generally wanted funds in my taxable account, with an average total return history of over 3%. Both BTMIX and DBLSX can have TR years of over 3%, but they usually revert back to their "safe" but lower TR. I have held NVHAX periodically in the past, but it is more volatile and risky than BTMIX"
FD:Looking at short-term duration Muni funds NVHAX,BTMIX,VMPAX,ORSTX. For 3 year performance, Portfolio Visualizer (link) shows that NVHAX performance is 2-3 times better and it's SD=1.5 was worth it and why NVHAX Sharpe ratio + Sortino are much better.
dtconroe: I have already stated the "reason" why we are looking at very conservative bond oef funds for my wife's IRA."
FD: My post was about your use of BTMIX in a taxable account per your post earlier.
BTMIX had a good year? YTD it made only 3.96% while NVHAX made 7.65% and many inter-term Muni made over 10%.
Why would any reasonable retiree go for a long term of 3% performance for their whole taxable account?

I am grateful for learning about mutual thrifts from reading one of Peter Lynch's books many years ago. He listed a large number of these thrifts (usually savings and loans) in his book. I was also able to identify around 100 more on my own, and as a result I went on a mission of becoming a depositor/part owner of several thrifts that eventually went public, offering their depositors the opportunity to participate in their IPOs. I never lost money on any of these IPOs. Thank you, Peter Lynch. (Unfortunately, this game has essentially run its course now that only a handful have not gone public.)

I am a few years out but now I am a “young” retiree so I will now have 5 years before my first RMD. Plus the chart gets reset so those taking RMDs already will reset lower next year.

Gary: "...you may not need to start RMDs for your wife next year. Depends on when the SECURE Act kicks in."
At Fidelity, at least, it apparently already has. I had mine setup on auto pilot through Fidelity to start in 2020. One 5-min phone call was all it took to move it out 2 years.

Hi catch22, thanks for posting. Yes, we are aware of the various options for how you take the RMD. I have been taking RMDs for several years, and have done it a couple of different ways. When we transfer the RMD money to our taxable account, we have a variety of fund options in our joint taxable account, where the money can be invested and grow with minimal to no tax consequences, or we may choose to use that RMD transfer to pay for some large expenditures that are due at the beginning of the year for us. There are pros and cons to the various strategies of how you harvest the RMDs, so I certainly see why various individuals choose the approach that best fits their particular situation. With regard to what my wife and I are considering for her Traditional IRA, we have not yet decided what we are going to do, but diversifying a little more is what we are now looking at.

I missed much of this conversation--had a family Christmas gathering tonight. I just started posting on this forum, after years of posting on M*. This thread is very much in line with two recent threads I started at M*, in which I used the same posting name. I made a post at M* that I was going to start posting on the MFO forum, and invited others to join me, including Gary1952 and Craignw. MikeM asked what OEF stands for--Open End Fund. Craignw, nice to see you posting here and hope ZEOIX works well for you. Mona, thanks for the kind words. For those who do not know me, I look forward to getting to know each of you, and look forward exchanging ideas and sharing information.

Hi,dtconroe
Back in late November 2018, you spoke about several funds, of which ZEOIX was one. Usually high yield is too volatile for my investing choices. I researched this fund and found it to be in my wheel house after all. I bought 5000 shares in November of 2018. It has posted a return of 5.33% ytd. The fund has a low volatility with a duration of 0.88 years. My nav in the fund is up since purchase, with a nice monthly yield.....thank you for the heads up on this fund.
craignw