Aww…the poor bunny. I’m so glad you are helping him. I would suggest avoiding a bath since it is extremely stressful to a rabbit and this little bun is probably stressed enough. You could try corn starch. Put some corn starch in your hand and rub it in the dirty areas, then comb out the excess. This should help safely freshen him up.

Now that he’s out of the elements he will probably be able to keep himself clean. Are you planning on keeping him?

I think after spending some time resting with you, and using the corn starch, he may be comforted enough to risk a bath.
Make sure it’s not in a cold room, and that you have a big towel handy.
I would put an inch of warm water into a tub or set tub, or sink if you can hold him there very well. Use a cup to wet all but his head, ears and face. Use a warm washcloth with unscented, mild soap or baby shampoo and gently hold him and soap him up. Rinse him off with the water there or slowly run warm water in a stream from the faucet to rinse off using the cup and washcloth. He may struggle so be very careful he isn’t in a place where he will fall if he gets away from you. (A tub on the floor is harder to maneuver but safer if he runs.) Once rinsed, put him immediately into a towel and burrito him so he is completely wrapped except for his head. Hold him as you rub him dry. (A hair blower on low setting may be a scary noise, so only use it if he is calm later and not dry enough by towel.)
While he is definitely stressed already, if you talk soothingly to him the whole time and are firm but gentle with each step he shouldn’t be shocked by the ordeal enough to be sick or harmed, and will feel much better once he is cleaned. You probably won’t get all ground in grime off, but if the surface dirt and odor is better, he will clean himself after you dry him which will also help. He may need one more corn starch sprinkled bath after that, but this should help. Put him into a nice blankie and covered hidey place, like an overturned cardboard box, where he can rest afterward and feel protected and warm.

Any update on how this one is doing?

Thanks for taking him in! He seems like such a sweet little thing ? along with LPT, do you know if you’ll keep him?