DS2 was 9 months when he started daycare and was having EBM bottles there. He was still very happy to have boob when he was at home though. And formula doesn't taste as good either... why would they refuse lovely sweet BM and mummy cuddles to get formula in a bottle?
If 1 formula feed a day gives you the break you need to get your nipples back into shape then do it, but it doesn't mean the end of BFing!

Both my boys had all their teeth before they stopped feeding too, and I only ever got bitten a couple of time. They work out pretty quickly that biting means no food and they stop doing it.