...I wish I could help with this...all I can say is you're not alone. My dd is only 13 mos and bites me many times a day. She rarely bites her father and as yet has not bitten anyone else. I just put her in her crib for 'time out' since she also either bites harder or laughs at me when I say no or tell her that it hurts and is not nice. I too resist the urge to hit her, as I can put up with almost anything, but when someone is deliberately hurting you, I think it's a natural defensive feeling to want to 'hit back' that requires all of the patience I can muster to resist.
Mostly she does it for attention when I'm trying to get something else done, or in anger for not getting what she wants. Sometimes she gets so excited playing that she starts in (which is what just landed her in the crib). Sometimes I get the feeling that she's trying to express affection (in an open-mouth type bite where she doesn't actually chomp down), and just doesn't exactly know how to kiss yet.
I don't know what to do either...she went through a stage where she bit me while nursing (that was awful), and that stopped after a while, but I was able to cut her off from the milk each time, which eventually gave her the message that it wasn't going to work to keep that up.
I hate putting her in the crib as time out, as that's her bed too and I don't like to associate sleep with punishment, but it's the only safe place I can really put her to get the 'time out' thing across.
Sadly, we have no friends with children under 1 hour away...family is further than that, etc. I need to find a place where she can play with other kids and get some time without me as her only companion. I think that will help somewhat, as I think she's just bored with me to some degree.
If you figure anything out, let me know!! I just wanted you to know you're not alone...