Wild rabbits do bite and can draw blood when they do so. While their speed and agility is their primary defense mechanism, if cornered a wild, scared rabbit can and will bite very hard.
So what should you do if you come across a wild rabbit that is trapped or stuck and you need to pick it up to move it?
A pool net, for example, is a nice, safe way to pick up a wild rabbit if necessary.
Rabbits are fast, so you should grab the rabbit around the body if at all possible. Then, as quickly as you can, pick up the rabbit by the scruff of its neck.
If you feel the area is not safe, you can either relocate the animal to a nearby wilderness area or contact a local wildlife rescue for further advice.