HI S.,
I work with chldren and want to let you know this is a phase many kids go through. I encourage you to remove her from the situation and tell her "Its not okay to hurt your friends. Mouths are for talking and kissing, not biting." Keep her in a "time-out" for one minute (one year for every year of age is recommended); then remind her to use her mouth nicely.
Sometimes kids do this when they are frustrated, so you may want to watch what happens just before she bites. If you can anticipate she is going to bite, stop it before it happens and tell her, "I see you are frustrated that Molly is playing with the doll. You can have it when she is done. Let's play with the ball now." This stops the behavior, gives her a better solution so she knows she will have a chance and redirects her attention to something new. Labeling her feelings helps her understand what she is feeling. She is too young to understand everything you are saying, which is why the redirection part is so important. As you keep using this approach, she will learn how to share, how to use her words, how to label her feelings, and how to cope.
Use the same approach, but different words as she botes her daycare provider. "You are mad that its clean-up time. Its not okay to bite. Let's put the balls away." Reinforce when she does share. Praise her.
Please don't bite her or have her bite herself. This is not effective. She does not understand that her biting hurts and this is not the way to teach her. Biting her will teach her she cannot trust you and that you may hurt her. Ouch. She is most likely biting because she does not have the words/social skills to handle the situation any other way and biting is often effective. When she bites a child who has toy she wants, she bites, the other child drops the toy and she gets it. Not appropriate, but effective. By using the approach above, she learns the social skills.
Good luck!