I can't avoid a woman I work with who has been extremely rude to me from day 1, what can I do?

Thicken your skin. One thing is certain, one can't change other people's behavior. Some choices? First, whose day one was it, yours or hers? If it was hers, being new she may be obvious to all operating rudely and self destruct. If it was your first day develop a thick skin, work hard, establish your own reputation and let your good behavior cast a bright light on her rude behavior and again may self destruct.
What do U mean ? People u work them can have different characteristic , u don't have to like them but u need to work as team to make sure the work is done to the best of u ability. If there are other issues discuss with u supervisor.