For some reason this question has come up a lot lately. I thought I'd save myself some time and answer it here, so I can just post a link. I've nursed five children, each for over two years. So, I've been bit once or twice. I have some experience with it. You are not inevitably doomed to bleeding sores.
Babies don't all bite for the same reason. Figuring out why your baby is biting can help end it. One overarching thing to keep in mind is that it is anatomically impossible for babies to get milk and bit at the same time. If they are nursing, they can't bite. If they are biting, they aren't nursing.
Some babies bite at the beginning of a feed. Often they are seeking pain relief for swollen, tender gums. It may take some timing on your part, but try to sooth those gums before baby is very hungry and just before feeding. Offer a teething toy, a wet frozen washcloth, or rub his gums with your finger. Relieving the pain may help him, and you, have a better nursing experience.
Other babies will chomp and release toward the end of a feeding. Go with what feels natural in a situation like this. Let out a yelp! Immediately remove her from your breast, firmly tell her, "No biting!", put her down on the floor and walk away, even if she is crying. In generally, a Christlike mommy doesn't want her babies to cry, but in this case, loving discipline is in order. Come back soon, soothe her and remind her, "No biting." Babies learn quickly, that biting means no cuddles and no milk.
Some babies bite at the end of a feed and latch on like a little barracuda. They just won't let go! It seems wrong, but pull that babe into your breast smothering her. Make sure to cover her nose, so that she can't breath, so that she is forced to open her mouth to breath. Don't worry, you aren't trying to strangle her, just force her to open her jaw! She will. Like above, immediately firmly tell her, "No Biting!", put her down on the floor and and walk away. She'll get the message after repeatedly doing this.
There is another class of babies that seem to get bored toward the end of a feeding and bite to get a reaction from you. For these little ones, watch closely for when they start to slow down. Unlatch them when they are near the end of the their feed and end the feed a tad early. This can be tricky. You want them to get enough to eat, but not bite you. Usually, a babe this age is older and also trying out solid foods, but getting his or her main nutrition still from mama. But, you've been doing this for a while, and probably have a feeling for when your babe is getting full.
With any of these, consistency is the key. It may take a week or so of repeatedly teaching your baby. But, it is so worth it. Nursing an older baby is so much more fun and rewarding than nursing a newborn. Plus, it makes life a ton easier. Looking back on it, getting through the biting part was actually easier than getting through the newborn part. You've made it this far. You've got this Mama!