Answer:
If the bite is that bad, it is probably best to take bunny to a vet for medical attention. Bacteria in the other animal's saliva or from the environment could cause a nasty infection, or the wound may require stitches to close.
Otherwise, make sure the bite is clean; wash the area gently with a mild soap, removing any dirt and debris, and carefully trim back the fur if possible. Gently press a clean gauze pad against the wound to stem any bleeding. Once any bleeding has stopped, leave the wound open, as bunny would probably tear off any dressing you attempt to affix.
A dab of a mild antiseptic or hydrogen peroxide might help, but be extremely careful to keep it away from bunny's eyes. Keep a close eye on bunny to see if any swelling or redness develops, or it becomes ill and lethargic. If so, seek medical treatment.