Direct Bus Munich to Rothenberg ob de Tauber

Rome2rio can't find it. You will either have to convince your wife to hop on and off trains or rent a car.
I do see transfer services for 500 EUR.

I am in my late 70's. I appreciate not liking train transfers but they do work. Best if you pack light and are at the door waiting to get off when a train pulls into a station.

I see there is a route through Treuchtlingen and Steinach (By Rothenburg ob her Tauber) with just 2 transfers at 9:35 in the morning.

There is another with just one connection at Steinach... at 11:35am. The Steinach connection is pretty automatic, just follow the crowd through this very small station. There are stairs.

https://int.bahn.de/en/offers

Thank you both for your help.

There is another with just one connection at Steinach... at 11:35am.

I'd take just this one, it's the right train for old people like us (it's not called for nothing the "Kukident Express" among railwaymen - K. are dentures cleaning tabs ;)). It takes seniors from Berchtesgaden directly to Munich and (almost) to Rothenburg and finally to Hamburg - all at an extremely leisurely pace. Don't be surprised if it stands around for half an hour in Augsburg, it's waiting for its sister train from the Allgäu, which brings the other half of its retired passengers.

Don't worry about changing trains in Steinach; there is no lift but there are conveyor belts, and the distance to platform 5 is very short. Otherwise, just ask someone for help. Franconians are usually taciturn, but helpful.

This popped out at me...

...my wife is not a fan of hopping on and off trains with luggage with multiple transfers.

It sounds like you are a good listener. So I will just encourage you to listen carefully to Rick Steves' advice on packing, to "sell" this advice to your wife, and to follow it yourself as well. This advice, IMHO, represents Rick's largest contribution to the world of travel.

There is nothing worse than a debilitating ankle or shoulder injury. Your wife is very wise to be concerned about lugging luggage. But train station transfers are NOT the most serious concern when it comes to safe luggage handling, IMO. Trains and stations these days have often been built and re-built to be far more accommodating, generally speaking, than they were a couple of decades ago. Negotiating several blocks of unfamiliar streets and sidewalks, using staircases in hotels, walking over cobblestones, and the lifting and lowering of your bags on both planes and trains may also be cause for concern if one or both of you is carrying too much weight or handling your bag less than thoughtfully.

I do not advise limiting your train travel to only direct trains as others have done. If you can walk with your bags at a fairly normal pace, you should be fine for making your connections. You should practice walking with your bags at home before leaving over several days to allow your body and bag to adjust to each other. Walk some stairs and practice opening doors with the bag to get the hang of it, etc.

https://www.ricksteves.com/travel-tips/packing-light/packing-smart

The German equivalent to Greyhound is Flixbus. Very popular with people for whom price trumps everything, even personal safety.