The lake region is small enough that bicycle and bus, in combination, get you everywhere. A regional bus runs from Bohinjska Bistrica through Ribcev Laz and on to Ukanc and the Savica trailhead, hourly in summer and several times a day in winter. The Bohinj Card (sold by accommodation providers) covers the buses and several other services and is worth it if you stay more than a couple of days.
Cycle paths run around most of the lake and along the Sava Bohinjka river to Bohinjska Bistrica. Bicycle hire is easy in Ribcev Laz and in Ukanc. A car gives more flexibility for further afield — to Bled, the Pokljuka plateau or the Soca Valley — but you do not need one to enjoy the lake itself.