They move in circles. As soon as you see one, STOP MOVING. They'll run for a few yards, until they're out of direct line of sight, then stop. If you stop moving and wait for 1-2 minutes, they'll calm down and start browsing again. I find it very difficult to do this, because I feel like I can raise my gun and take the shot before it sees me, but I almost always rush the shot and miss, or it sees the movement and runs. Be patient. (Something I need to work on) When you move, move slow and steady, and try to time your movements when they're looking away. If you wait long enough, they might just forget you're there and wander back into your line of sight. Then, raise your gun very very very slowly, and take the shot. This is for cottontails. For hares, it's a bit trickier, because they tend to just book it when they see you, instead of stopping They still circle back, though. If you see one, sit down and wait for 20 minutes or so. He might come back around and give you a shot.
Also listen to
>>674107. They hate the suspense. And they'll try the same tactic of trying to sneak back the other way on you (like I said, they move in circles.)
Alternatively, you could find a well-used rabbit track and just sit and watch it for a few hours. There's a good chance you'll see at least one wander down bunny highway.
Good luck to you. Bunny hunting is great practice for hunting larger game. Don't give up, and eat what you kill.