He may not be able to clean himself properly with his dodgy teeth either - Mary's fur would get very haggard looking when his incisors were due to be burred (before they were removed)
You can use some cornflour as a dry 'bath' - either rub a fair bit in to his back-end and brush it out, or if you're brave you can add water to make it into a paste to apply, let it dry then brush it out
I've bathed bunnies but they really don't like it - I ended up wetter than they did :lol: But if you really have to do it I'd recommend what I do with all the little critters I bathe that don't like the water - fill the sink with lukewarm water (you can add a little pet shampoo to it if you want), have an old towel folded up next to the sink. Dip the bun's dirty bit into the water, massage it quickly to get the water all the way down to the roots of the fur, then put the wet bun on the towel. Add shampoo and lather it up, then dip them to rinse the majority of the bubbles off. Put back on the towel, then fill the sink up and dip/massage the rest of the shampoo out, all the way down to the skin (as animals have sensitive skin, if you leave some shampoo on it can irritate them). I usually then empty the sink and use a jug just to pour a bit more clean water over them to rinse off any remainders, then towel-dry them off. I'd keep him indoors while he's damp so he doesn't catch a chill - you can (carefully) use a hairdryer but it needs to be used at a distance, I find towel-drying much easier and less stressful.