The best bet for public transportation is to take a bus through Bled onto Ribcev Laz. We got on a bus in Ljubljana, through Bled, through Bohinj Bistrica, on to Ribcev Laz.
The train also comes down from Salzburg through Lesce/Bled, where you will need to hop a bus anyway to get to Ribcev Laz
To get from one side of the lake to another you either need to walk or hop a bus. Check at teh Tourist Office if you can't figure out the bus schedule.
We did both. We took a bus one time from Ribcev Laz to Ukanc, then we walked another time. Stara Fuzina to Ribcev Laz is definitely walkable.