Regional pass

Hi hampmike, and welcome! The Regional-Pass Bernese Oberland covers part of the trip Zurich-Mürren. The map under the link 'Overview of the network on which the Regional-Pass Bernese Oberland is valid' at this page shows the area of validity. If you travel via Lucerne and Meiringen (which I'd suggest, as it's a beautiful route) the pass will be valid from Lucerne, allowing a 50% discount between Lucerne and Brünig-Hasliberg. Between Brünig-Hasliberg and Mürren either a 50% discount applies on non-free travel days, or free traveling on free travel days. Whether this is an economical choice, depends on your plans once you're in Mürren. If you plan to make lots of trips involving public transportation in the Jungfrau region, the free travel days offered by this pass are definitely worth your money!

Yes, the trip from Mürren to Venice requires several changes of trains: at Lauterbrunnen, Interlaken Ost, Spiez (sometimes Brig as well, depending on your train connection) and Milano. Your Regional-Pass will be valid up to Brig.