We are using Bayern Tickets for Germany and a rail pass for Switzerland, but are concerned that our trip from Ulm to Interlaken will not be covered by these passes. Any thoughts?
Your Bayern ticket is a 2nd class ticket. I think that it may be for regional trains but I'm not sure. If yes, you may need to pay a supplemental fee to get on the express trains to Switzerland.
For your Swiss pass, a properly validated pass will cover you from the border (i.e. Basel) to Interlaken. Note that your Swiss pass must be validated - especially a flexi-type pass. Make sure that you don't show the conductor an unvalidated pass or a flexi pass that does not have the day of travel inked in. They frown on that kind of stuff.
Yes, the Bayern-Ticket is for regional trains only. However, although express trains don't go everywhere regional train go, regional trains go everywhere express trains go (albeit slower).
The fastest way from Ulm to Zurich is usually via Basel - and that's through Baden-Württemberg. A Bayern-Ticket won't work but a Baden-Württemberg-Ticket will. Same price, same conditions as the Bayern-Ticket except in the state of Baden-Württemberg, not Bavaria (Bayern).
There is no such thing as a supplement with the Bayern or Baden-Württemberg tickets. If you want to ride express trains, you must buy a full fare tickets for those trains.