On our bike tour we found nice bed and breakfast establishments "Private Zimmers with Zimmer Frei signs" on our tour without reservations.
Every year over 380,000 people ride bicycles around Lake Constance. Of that number, only 10,000 do not have advance reservations. If you are traveling during the high season of July and August, calling ahead at least a day, would be advisable. Even safer would be to take a guided tour that would book your accommodations. The extra money might be well worth it. We went in early June and there is plenty of capacity.
This is more of a hotel but not too bad price.
http://www.adler-immenstaad.de
Price per person per night with Breakfast: 36 till 38 EUR