I've given this some thought and I'd be curious for some feedback. I'll use Kansas to illustrate my point.
In the US, too far east and you get into a close network of cities. Too far west and you'll end up in the desert. Too far north or south and you'll have to jump around seasonally. Kansas is flat and that's important because it allows you to cycle over longer distances. if you're willing to bike camp, you can put yourself further away from civilization.
Pick your spot, or spots on the map. Clumps of forest and lakes or some state parks. Choosing Kansas as a recreational destination for camping isn't high on anyone's list. It's something you do because a) you live there are don't want to leave the blessed state or b) you're passing through and are forced to stop. You're going to meet less people there than places known for their magnificent vistas.
If you need to move around, there's farmland too big to cover with surveillance. If you want to stay still, pick a larger city for day labor. Stock up on supplies and hit the road on your bike. With just a day, including stops for rest, you can get pretty far away from cities and towns... probably find a nice state park or even wooded area on the previously mentioned farmland. Hillsdale State Park is a 50 mile bike ride from downtown Kansas City, for example. I've been out there - never tried to live there, but it's awfully nice and you can see the stars pretty well. There's a lot of unfriendly patches along the generic google maps cycling route, but also a lot of bike trails in that area. Research would make the journey better. I like the metropolis areas, so that's a spot I think of when I dream of a plan like yours.
Good luck!