Another idea is to ride down to Interlaken and jump on the #8 bike route that goes along the lake of Thun. This is quite a scenic ride and relatively easy. You can continue on this route all the way to Bern if you like. Bern - Basel by train is about an hour.
If you want more of a challenge you can take route #61 on the other side of the lake. I haven’t done this one but it looks like you can hook up with it already in Zweilütschinen (if coming from Lauterbrunnen) or do what WengenK suggests and connect with it in Grindelwald.
A helpful resource is Switzerland Mobility. Here you can find all of the cycling routes. The app is free, but if you are willing to fork out the yearly fee 35.00 CHF you can then draw your own routes. This is what I do because I often want to combine various routes and this way I can see exactly what I am dealing with.
Even with the free version you can set it to show all train stations, click on the icon for the station you are interested in and you will be directly connected to the SBB schedule for that stop. Some trains require you to have a reservation for your bike, but the SBB app will show you that when you choose your train.
https://map.schweizmobil.ch/?lang=en&photos=yes&bgLayer=pk&logo=yes&season=summer&resolution=250&E=2636500&N=1208400&detours=yes&layers=Veloland