There are some marked mountain bike routes around Gimmelwald and Muerren. However, this is not for comfortable bikers, because it either goes up or down - flat is not possible on the mountain terraces. For leisurely bikers, the best routes are the ones exploring the valley floor between Lauterbrunnen and Trachsellauenen. An alternative option is the ride out of the valley towards Interlaken.
Bikes (traditional or electric) can be rented from Imboden Bike in Lauterbrunnen: www.imboden-bike.ch
Advanced mountain bikers complete the downhill section of the Gruetsch Trail from Gruetschalp down to Lauterbrunnen. https://muerren.swiss/de/sommer/tracks/gruetsch-trail/