Here are the instructions for a dry and a wet bunny butt bath: http://www.bio.miami.edu/hare/buttbath.html
You could try using a wet washcloth. If you use any soap, make sure that it is mild and hypoallergenic. Two bar soaps that are mild and hypoallergenic and come in unscented varieties are Kirk’s Castille and Clearly Natural. I use both of those soaps on myself, and cut off a tiny piece if I have to give a bunny a butt bath. I haven’t had to do it in a while. I did it a few years ago for a couple of elderly bunnies on occasion, since they couldn’t keep themselves clean. I used a plastic dish tub, and set it on the floor, not up on a counter, to prevent any any rabbit from getting hurt in case they jumped out. You just use an inch of water, and can have the little piece of soap in the water. It’s very helpful if you have someone with you. One person to hold the rabbit in the tub, while the other splashes water on the dirty area, massaging it to get it clean. If you use soap, pour out the first tub of water and put an inch of clean water to rinse. Thoroughly dry your rabbit. You can even use a hair dryer on low if you don’t think it would scare your bunny.