I do quite a bit of rabbit hunting, usually getting out four or five times a week after work for an hour or so- it's my winter exercise. When I take the dog and gun or bow, the shooting is fast with the rabbit usually way out in front of me. What I've personally noticed is that the shots tend to lend themselves more to hunting with my bow when I'm out hunting by myself. So don't let not having a dog discourage you from getting out.
As other have emphasized, walking slowly is important, for sure, but it is especially important in or near the thickest cover you can find. Be sure to stop OFTEN and stand still for a minute or two. Here's the thing: Rabbits often tend to bolt JUST as you start to move again. So, as you start walking again, take just a step or two and EXPECT a shot to occur at this moment. Try to stop next to fallen trees, bent over patches of thick vegetation or switchgrass, or a group of several thick bushes all clumped together. Often you will notice bunny trails radiating from thick cover and try to position yourself facing down these trails. It goes without saying to stop where you have at least a prayer of squeezing your arrow through vegitation. If you're serious about getting a shot off, have your fingers on the string, have the bow partially drawn (often you simply won't have time to draw your bow back) and BE READY to let 'er rip.