I use wood arrows with the big rubber blunts, and always aim for the eye. Walk real slow through the brush, and stop and look around every so often. It's all sagebrush here, so I really examine under every bush to try to catch one sitting there. A lot of times, especially when it's rainy or cold, cottontails will sit tight and won't move for nothin'. They will let you walk right by. If you do spot a rabbit within range, resist the temptation to snap into an aggressive position. If you're walking and you suddenly stop and bring the bow up, the rabbit knows you've spotted him, and he'll be gone like a rocket.
If I spot one that's too far away, I try to get closer by walking in an arc around him, or at an angle to him. Not straight at him.
I love hunting bunnies with a bow. It's challenging and fun, and if you're in good rabbit country, you get to fling lots of arrows. Our cottontail season doesn't start till October. We can shoot jacks all year, though. I have the best luck in the evenings, generally. However, mornings after a light snow are good, especially after it has started to warm up slightly.
HTH