Bettas' tails don't bleed. If it's red, I'd have to agree with Dorn that it sounds like tail rot. What may have happened was that the bitten part got infected. If it's getting worse, you may want to consider mediciating the tank for tail rot.
Unfortunately its often impossible to stop a biter. You can try moving him to a low-stress environment (not many people, no bright lights, no loud noises, etc). Or you can try showing him a mirror to flare at for a 1/2 hr each day, in case he's bored.
But if you're not able to stop him from biting, its important to keep his water extra clean. I had a tail biter for a year, and I was never able to stop him from doing it, but I always kept his water in decent shape, and he never got infected. It is possible for a biter to live a long, happy life.