Can you change your location and stay in Mürren? I know I’d like that more than a bustling city.
If not, trains are super easy. Go to https://www.sbb.ch/en and enter “Bern” and “Mürren” and the date. You will see it it’s about a 2 hour journey with 3 or 4 changes. Not to worry as those changes are easy. Here’s the most efficient route leaving at 8:04 and 9:04:
Bern Bahnhof to Interlaken Ost, change trains, 8 minutes to do so which is plenty of time
Interlaken Ost to Lauterbrunnen, walk across the street from the station to the gondola to Grütschalp, 13 minutes to do it but don’t dally as the lift gets full
Gondola up then change to the little mountain train that takes you along the cliff to Mürren. Arrive 9:58 or 10:58 depending on what time you left Bern.
You can return to Bern by simply reversing or take lifts from Mürren to Stechelberg at that end if the valley and then catch the Post Bus back to Lauterbrunnen Bahnhof.
Will you have a Swiss Travel Pass of any sort?