Babies can bite while nursing regardless of whether they have teeth. It hurts more with teeth then without. It's funny in the beginning without teeth. It's much less funny when the teeth start popping up.
Can it hurt you? Yes, but probably not to the extent that you need to stop nursing. Whether you want to stop nursing because of it is a different matter.
What if I'm bleeding? Nipple cream is your friend. Blog in your milk is okay and will not hurt the baby. If you can, nurse or pump through it. It will feel better with time.
Can I teach my baby not to bite me? You can try! I tried, but it never really worked. She would still bite at the end of nursing or when she thought I should be paying attention. At times, it even made me angry--it hurt! But I swallowed my frustration and kept nursing.
Does it ever stop? Yes! And then you think you're out of the woods, and it can begin again! The important thing to remember is that biting is a symptom of teething, and that when the teeth and jaw feel better, the biting will stop. If you can wait it out, it could be worth it!