While stealth camping is fun and worthwhile, you don't have to find a rough patch of woods in order to camp. On my tour this summer I always found small town parks and churches in the country as good places to set up a tent. Most of the time no one was around, so I didn't ask, but no one noticed anything and I left without a trace.
You should try to ask if you can stay in a church lawn or town park, but if you can't you wont be in any big trouble. Small town and country people can be very nice and they'll most likely be too curious about you as a traveling cyclist than they are worried about you camping for a night.