You start off in the harbour of Constance with the Catamaran to Friedrichshafen. You can take your bike with you on the Catamaran. From Friedrichshafen to Lindau it's about 27 kilometers. The path is flat and you cycle through the nature reserve "Eriskircher Ried", via the castle Montfort and a nice village called Wasserburg.
If you go on, you arrive in Bregenz about an hour later. There are renowned cultural events in Bregenz, as the "Bregenzer Festspiele", which is an opera with the stage in the lake. But the town itself is not so interesting. Especially near the lake, Bregenz is rather ugly. But it's really worth to go on the mountain Pfänder (1064 meters, there is a cable car). You have a good view on Lake Constance from up there. If you want to go to Bregenz for the "Bregenzer Festspiele" from Constance, you can book direct ship trips there, which is really nice.
If it's not too late, you can return from Bregenz to Constance by ship. But the last connection usually departs quite early in Bregenz. And the train connections are a bit complicated (you have to change the train quite often and the author of this article failed to buy a ticket to Constance at the ticket machine at the railway station in Bregenz). From Lindau, it's easier to return to Constance by train.
You can also go to Lindau and Bregenz by ship from Constance, both ways. But the excursion-ships of Lake Constance are quite slow, except of the Catamaran from Constance to Friedrichshafen. But it's both better, than going by car. We think, that going by bike is real fun at Lake Constance and the best way to see the beautiful landscape.