I read a few responses and it seems that everyone is under the impression she's biting you. Somehow I'm doubting that's the case! You did say it's tolerable, and biting certainly is NOT tolerable.
My guess is that her teeth are simply rubbing on your nipple/areola too much and making things sore.
I went through this with my older girl (and am bound to go through it with my younger one too since she's even more of a booby hound than my first!). The only thing you really can do is adjust her latch. She'll have to learn to open up a little more so her teeth aren't touching you continuously. It can be done! Otherwise we would've evolved to get teeth much later than children are meant to breastfeed.
I know it can be done because I, like MANY moms, am still breastfeeding my 2-year-old (What's really fun is if you find yourself PREGNANT and breastfeeding a mouthful of teeth! Nipples get sore without provocation, and here's constant aggravation!). She has a set of 14 teeth. I think once they get a few more teeth it may get easier for them too, because they get used to opening their mouths more to accommodate for the teeth.
As for the bottle... that could be confusing her more! She's allowed to bite on the bottle and she isn't hurting anyone if she's closing too much on it.
Another hint for adjusting the latch: change the angle at which she sucks. I did this with my daughter, bringing her chin in a little more. You may need to play around with it a bit. It's just like when you begin BFing: there's a learning curve and you just have to figure out what works. Maybe talk with a lactation consultant briefly or contact La Leche League for a few more hints.
No need to give up what nature intended for you!