My oldest (now 3 yr old) son did the same thing! He probably bit me a couple hundred times throughout the almost one year that I nursed him. I tried everything to get him to stop (I flicked him, yelled ouch, ended his feeding, etc, but he just was a biter.) I noticed he mouthed and bit EVERYTHING, though, it wasn't just me. He aslo was a pacifier user. I think some of it had to do with teething, but he was just a "oral gratificiation" baby, one that loved feeling things in between his teeth and gums. Ha ha. He also ate for a long time began playing around when he would start to bite me. When he was really drinking I don't remember him biting. So, I had to really pay attention and try to watch for the signs he was about to do it! Then we would end the feeding done or not! This probably is not much help to you, but I hope to at least let you know you are not alone. I didn't end my nursing relationship because of the biting but every time he did it, I let him know I didn't appreciate it.
My younger one (now 21 mos) bit a lot too, but he always cried when I informed him he just hurt me. His was clearly due to teething, and he didn't use a pacifier or really use his mouth to "mouth" things as much. He also ate very quickly (pretty much less than 2 minutes on each side). He was all business. But, as soon as he was done, if I didn't get him off, CHOMP! And, if my milk didn't let down right away, CHOMP!
Good luck with your precious baby! :o)