After watching RS do a bike rental in Murren we thought it would be a great thing to do...and it was, but a word of caution. I don’t think RS actually rode from Murren to Lauterbrunnen via Gimmelwald as that route is extremely technical in nature. Likely this was just a staged photo op. The best route is to go from Murren towards Lauterbrunnen via Grutschalp then from Lauterbrunnen to Stechelberg. From there you can tram all the way back to Murren. Bikes generally cost 1/2 of a fare. Fro Murren to Lauterbrunnen You can also detour to Isenfluh and then onto Stechelberg. We decided to ride from Murren to Stechelberg via Lauterbrunnen and then back to Lauterbrunnen taking the tram up to Grutschalp (40 chef for two people and bikes) and then ride back to Murren. You could also take the train back to Murren if you are Knackered. This ride is 31km, and is mostly easy but there are two stretches of about 300m each way that have a very steep elevation gain. I ride all the time so it was no problem, but my wife found this to be a bit gruelling so be warned.
Bikes can be rented from Intersport on the main drag in Murren for 40chf for a full day. You can also rent E bikes in Lauterbrunnen as well which makes going uphill a lot easier.
Travel well!