I agree with Jersey except for the part about being raised up. While I have often used the bathroom sink with an inch or so of water, it was for a bunny that was disabled and used to butt bathes already.
For my young and feisty Spockie who had poopy butt on occasion, I opted to put an inch of water in the tub. It’s a bit harder to lean over, but you can hold him firmly in place (or even better, have someone else place a firm hand on his shoulders and back for you.). He will run and squirm, but it’s hard for them to jump over the side of a slippery tub if they get away from you and if they do, it’s not a big fall.
Warm water, then take a washcloth or just your hand with mild unscented soap or baby shampoo (nautural stuff, unscented, not like Johnson’s) and gently rub under their butt and belly while he is standing in place. DO NOT get his head and ears wet at all. You can turn on the faucet lightly to rinse off your hand and cloth and just splash a fresh water rinse underneath to rinse the soap out. You could drain the tub first, but that takes a while and he’ll be wet and uncomfortable, so wiping down the soap and splashing it off is quicker.
Then out into a waiting towel, on someone’s lap or spread on the floor where you can lift him out and wrap him up quickly. Towel dry first, then blow dry on low, warm or cool setting. (Oops – Jersey said that already.
) The bunny will clean himself after, so if he’s still a bit damp it’s not harmful. You want him to be basically dry, but not get his skin hot, so stay at least a foot away with the blow dryer.
Then expect to see a pretty, clean backside as he gives you the bunny butt. He won’t be pleased until he notices he feels better. They like to be clean, so ultimately, they don’t mind the “end” result.