There is a cycle path around Lake Constance. It has an overall length of 270 kilometers. The path is well signposted. And if at some place, you don't know where to go: Take the lake for orientation. Just don't get too far away from it. Most of the path is situated really near the lake, but not all of it.By using public transport, you can easily split the whole tour into several one day trips. (Map with an overview of the tour).
For going around the 70-kilometer long "Untersee", you head off from Constance to Stein am Rhein (beautiful, historic city center). There you cross over to the other side of the river Rhine. Then you go on to Radolfzell and then to Constance. Just before returning to Constance you can make a detour to see the island Reichenau with its ancient churches and vegetable plantations.
When you are in Stein am Rhein there also is an interesting detour (about 20 kilometers one way): Don't cross the river Rhine, as described above, but just cycle on till you reach the Rhine Falls, right after the town of Schaffhausen. From Schaffhausen or from Stein am Rhein you can go back to Constance either by train or by boat (for the bike you need an extra-ticket).
The tour around the Obersee is about 200 kilometers long. The route is quite flat, apart from the section between Wallhausen and Bodmann and a section behind Ludwigshafen (in the direction of Überlingen). If you are in good shape, you can do the trip in one day. But there are quite a few comfortable shortcuts by public transport. You can use the ferry to go to Meersburg, the catamaran to get to Friedrichshafen, any other ship or you you travel by train. Usually it is no problem to use public transport with a bike, with one exception: Most busses don't transport bikes.
Which are interesting places on the tour for a stop?
There is the Marienschlucht, a kind of canyon between Wallhausen and Bodman. Then you shouldn't miss the baroque-style church Birnau. The
Some camping-sites are situated right at the lake. And you find quite many private rooms and hotels along the cycle path.