Though there's not much singletrack, this route covers some amazing terrain, even more amazing views, and with many options for food and beverage or snack breaks (mid-ride croissant, anyone?)
If you don't want to pay for the tram at the start, or would enjoy an extra 1,500' vertical climb, there are well-marked routes from Lauterbrunnen to the top of the tram that you can ride.
From the top of the tram (which takes bikes!), walk your bike up the short hill to the start of the Grutschalp to Mürren trail past a gate. Very soon, the views become just amazing, even by local standards. There are many southeast-facing fields filled with flowers, and it's hard to keep your eyes on the trail! The little trail that connects to Murren will rumble by once in a while, and there are some cows and hikers to look out for (in the first half).
From the midpoint of Mürren, take a left on the Mürren to Gimmelwald Trail and pass several working farms. Though both villages are "car-free" be careful of the occasional farm vehicle using this section.
The next section, the Gimmelwald to Stechelberg
descent is separated from the hiking trails, and is quite steep but rideable with decent brakes. Follow the red signs that indicate the bike trail. Follow many switchbacks, mostly through forest, passing by a great waterfall and over several bridges.
Once in Stechelberg, ride on the road a short ways, then take a left on the Lauterbrunnen Valley Trail
and pass below spectacular waterfalls back to town.