What happens if you bathe a rabbit and its head gets wet?

If a rabbit's head gets wet, it could get an ear infection.

Baths are not usually necessary for rabbits. Healthy rabbits bathe themselves, and as a matter of course you should keep them away from very messy areas. If your rabbit is messy, something is wrong! Baths can be very dangerous for rabbits, whether their head stays dry or not. See the related question below for details and links.