I have a book that describes a method for getting the dog to accept the collar without a fuss. I used this method on my dog because she would jump around so much that I could not get the collar on her. I can't comment on the biting because I don't have enough experience with dogs (are you sure she is not play biting?), but I can say that this method worked wonders on my overly eager puppie.
Get ready to go outside, tell your dog to sit/stay next to you by the door. Take out the collar and sit down to put it on your dog.
If she makes a fuss you stand up, say "oh well" and walk away. No reaction, just leave as if you couldn't care less. Go sit down with a book or the tv or something.
After a few moments (not too long) you try again. Go cheerfully to the door, try to get the collar on. If she does not sit calmly, you say "oh well" and walk away again.
Repeat until your dog sits still long enough for you to put on collar and leash. Try to be fast in the beginning.
When you succeed you give her lots of praise and a treat and hurry outside as a reward, make it extra fun to go outside.
This worked on my dog because she loves to go outside. And she is smart enough to realise that I won't go outside with her unless she sits still for the 10sec it takes to put on the leash. I felt awful for walking away from her without giving her the reward (the walk), but they are clever dogs, so she understood after three or four times. If she gets hyper now and I can't get the collar on, all I have to do is stand up and say "oh..." and she'll sit down before I finish my "well"
Hope I explained it so you can understand and good luck!
Edit: I just realized I don't know how old you puppie is and wether or not she knows "sit" well enough yet. Maybe my advise is too demanding, my girl was 6 months.
Have you tried a harness? Maybe she does not like a lot of action around her head.
Anyway, the best thing to to is probably to let a dog trainer or behaviourist to look at the problem like cazza sais.
