Bernina Express

rdrnnrbeep, The Bernina pass line (there is not just the Bernina Express on this line, there is one train per hour) is designed to get people over the Alps, so it is best included as part of your trip. Unfortunately you have a car, which you must get back to.

There are no large cities nearby (this is the Alps). The nearest big cities are Milan and Zürich.
You could leave your car in Tirano or Chur, depending one where you are coming from or going to.

Maybe you should reconsider your whole trip, so you don't have a car for the Alpine part, and you can include the Bernina pass line as part of your travel. Otherwise it would be very tedious to double back the same day to recover your car.
What is your overall trip plan / route?

Thank you for your quick response. We are flying in and out of Munich and were hoping to rent and return the car there due to cost. We are trying to include Salzburg, Vienna, Dolomites, Milan, Garmisch and Interlaken in our 24 day trip. I would really like to take the Bernina train line if we could figure out a way to efficiently circle back to getting our rental car. I've read so much about it that my head is spinning and what I've been able to determine, like you suggest, is that there is no easy way to accomplish this. Any further suggestions you can offer would be greatly appreciated.

We are flying in and out of Munich ..... We are trying to include Salzburg, Vienna, Dolomites, Milan, Garmisch and Interlaken in our 24 day trip.

rdrnnrbeep, That route is a big U - so far so good. Munich, Salzburg, Vienna (so far cities, where a car is a millstone around your neck), Dolomites (car good), Milan (car not good), Garmisch (this should be between Munich and Salzburg).
Now you are heading back north from Milan to Munich via Switzerland.
Now I go "off piste" and suggest what the Swiss would do, but the guidebooks ignore. On your way from Milan to Interlaken by road, DO NOT go through the road tunnels, but go "over the top" via the Nufenen Pass and Grimsel Pass. Do a google search for these names.
The Alps in Switzerland is two ridges, with a high valley in between, a 'M' in cross-section. In the old days (pre-railway tunnel) that meant crossing two high passes, which were closed in winter. You can still go the old route (in summer only), and it is as good as the Bernina pass, if not better.
Go to https://www.youtube.com/ and search for "Nufenen Pass" or "Grimsel Pass". Example: https://www.youtube.com/watch?v=exFZje9DnjU

rd,
The method I'd probably use in those circumstances would be to book a two night hotel stay and start in Chur. Arrive about mid afternoon, explore the town and then take the Bernina Express the following morning (reservations compulsory). Return to Chur via regular train, stay the night and then carry on with your trip. Be sure to choose a hotel that provides parking.

It's important to note that the panoramic cars of the Bernina Express only make two runs a day. The southbound train departs Chur at 08:32 and arrives Tirano at 12:45. The northbound train doesn't depart Tirano until early afternoon and arrives in Chur about suppertime, so that wouldn't be as convenient to get back to Tirano to collect your car. The regular train shouldn't be too expensive, but I haven't checked.

Also note that for bringing your German rental car into Switzerland, you'll have to obtain the Swiss Highway Tax Vignette or risk hefty fines. While not compulsory, an International Driver's Permit would probably be a good idea as well.

If you stick with driving in Austria you definitely are required by law to have an IDP. and an Austrian Vignette.

You can also plan to take a shorter portion of the Bernina Express. For instance, if you wanted to stay in smaller Thusis instead of Chur, you'd shave a half-hour off that end of the trip (each way) and if you make your turn-around at Poschiavo, you'd get 3 hours for lunch and looking around that town versus 2 hours in Tirano. I can vouch that you're not missing anything in Tirano.

Michelin and some other brands of driving map will highlight scenic driving routes with a parallel green line.

Thank you all so much for your kind replies. At this point we are taking the Bernina train off our itinerary but may revisit the idea if weather conditions due not allow us to take one or both of the passes suggested by Chris in his reply. It appears as though the Nufenen Pass is a definite no-go in May but that the Grimsel Pass may still be an option. We are hoping to travel the Grossglockner from Salzburg on our way to the Dolomites. Maybe that will help cure our need for high Alpine roads :) We will be traveling in May and are aware that some of the sights may still not be accessible. If anyone has had experience traveling during springtime in the Alps I would love to hear your comments and/or suggestions.

rdrnnrbeep, I was unaware you were travelling in May.
Most of the passes open in May, and close again in November. The exact opening date varies depending on how much snow needs to be cleared. They try to get them open for the holidays at the end of May (Pentecost).
Depending on when in May, and how much snow there was, you may find, one both or neither open.

This is the official website which shows the status of each pass: https://www.alpen-paesse.ch/en/