My view is biased because I live and mostly tour in an area with a lot of public land. In the mountainous western US, there's no need as a bicyclist to pay for camping. Free "dispersed camping" on US National Forest land is a well-accepted practice in many areas.

I plan my days to end in a place where the map is green and start looking for a place to lie down. If I'm planning ahead and that does not appear possible, say in a mostly agricultural or pastoral area or the rare city, I'll search the warmshowers.org network (I'm a frequent host).

A motel room once a week or so is nice. Maybe I'll pay for a commercial campground once a week if they have a tenting rate. Sometimes a local motel is only $20 or so more than an RV site.

Another class of camping not mentioned is the free town park. Ask at the local law enforcement station about that. Sometimes you'll get an escort and they'll check on your site during the night. (Once during a tornado warning, I got escorted back to the station to sleep inside.)