Munich to Rothenburg question

What does your itinerary look like for the rest of your trip?

This is always a hard question to answer given that it is really a personal choice. I would take the train over driving since the train station is convenient and you don't have to worry about parking the car. You can relax on the train. There is a lot to see and do in Munich so you could save Rothenburg for the next trip. The beer halls are great in Munich.

If you mean arriving in Munich from USA, no I wouldn’t sign up for a bus tour the next day.

Personally, I’d skip it and do something easy by train there are so many fun towns in the region.

There are plenty of places to see besides Neuschwanstein. I agree that it's a long trip for the first day there. You might want to consider Salzburg, which is beautiful and has so much to see and do. It's only about a 90 minute train trip and the city center is compact and very walkable. You can use the Bayern ticket from Deutsche Bahn to get there, which is a nice savings. I loved it there and spent 3-4 days exploring.

Not sure where you are flying from to Munich, but if you take a bus tour, you don't have to drive.
Normally, I would advise that you can do Rothenburg on your own, without a tour guide. The city is very walkable and easy to view with a guidebook.

Neuschwanstein is OK, but Rothenburg is better.
If you want to do something closer to Munich, consider King Ludwig's palace a HERRENCHIEMSEE PALACE, a bit south of Munich.

There are other options.
https://themunichguide.de/day-trips/castles-near-munich-germany/

If Wednesday is your first full day in Europe, I would not advise you to plan anything stenuous or complicated for the first day. Stay in town and plan something simple while you get over jetlag.

I'm pretty much of a DIYer, and deplore paying someone else to do for me what I should be able to do myself. Plus I don't like the inflexibility of an organized tour. So, I would not advise you to take the tour.

If you are arriving on Tuesday evening and won't be in town by Saturday, it sounds like you only have three days max in Munich. There is enough to do in Munich to occupy three days. Stay in Munich.

Save the rest of Bavaria for another trip(s). Come back again and see Bavaria (I've spent almost 100 nights there since 2000).

geovagriffith's suggestion for visiting Herrenchisemsee might be weather-dependent, but it's a sound idea, and you could do that ON YOUR WAY to Austria (assuming that's your next stop.) Use the lockers at Prien station, where you get off the train for the island-palace and its stunning surroundings:

https://www.mk-online.de/fileadmin/user_upload/news/contentstation/RoKa_17_BlickueberChiemsee_v0.1.jpg

That said, the handsome town of LANDSHUT (LAHNDS-HOOT) is quite close to Munich and could be a full-day or half-day outing. The train ride is direct and takes only 45 minutes.

https://www.tripadvisor.com/Attractions-g229466-Activities-Landshut_Lower_Bavaria_Bavaria.html

I am a big fan of Rothenburg but would not do it as a day trip from Munich. The town is most scenic and atmospheric in the late evening after the normal tourist rush has quieted. There are many scenic places with fewer crowds near Munich. Landshut is small -often overlook- town that is only 50 minutes north of Munich by train. It has great river walks, many beautiful old brick buildings and a castle.