What kind of rabbits are you hunting? Hares or cottontails?
For cottontails, I walk very slowly, and carefully search the brush with my eyes. Stop often. If any are near by, they get nervous when you stop, and they may take off. If they aren't too skittish, they'll go only a short ways and try to put some brush between you. If I'm too far away, or if brush is in the way, I try to pinpoint where the bunny is, then I walk away at an angle, and make a circle to get around the brush. Makes him think you're leaving.
Jackrabbits here tend to flush either long before you get in range, or at 60mph from right under your feet. Often they will stop and stand up and look back. But they only hold still for a few seconds, and they're often 30-50 yards by then, sometimes more depending on how spooky they are. If you're that good, it would be an excellent shot opportunity.
Buck-tamer, what part of Nevada are you from?