I second the comment about asking the local services for assistance with camping. East of Austin, it's usually hit and miss, but there are a few opportunities. West of Austin, you'll be fine. Some of the towns, obviously, are little more than a blinking light, so you may have to resort to asking people at a cafe, or whatever; in either case you'll be fine. As was the case for, I would be asked about my nightly arrangements at a store or cafe or whatever, before I had a chance to ask them.
There's a thread about Southern Tier camping that a few of us commented on a few days back that you might want to look over. Having just finished the ST I would recommend going at it with the idea if you're creative enough, you can swing a place to camp (which is likely true anywhere in the world.) As someone noted above, "pickign a tent" rather than camping is a safe way to think about it; I would just ask for a small plot of land, etc. It sounds more stressful, or harder maybe, than it will actually work out to be.
The local fire/police departments are more than open-minded about you camping for a night just about anywhere - local park, side of their building, etc. Again, same with Churches. Being on a bike is disarming (and comforting) for just about everyone you would end up asking, vs showing up with a huge RV in need of "hook ups..."