STOP! Unless she is doing something that actually hinders your work, I wouldn't go to the boss about rudeness. She may be reprimanded, but she very likely won't be fired, and she'll be worse than before, while you may get a reputation as someone who can't handle minor difficulties. Since you must work with her, ignoring her is not the answer; it will simply give her something else to complain about.
There is only one way to come out on top of this situation - kill her with kindness, in front of your supervisor whenever possible. Help her ONLY when she asks for it or when disaster is imminent. Do your job wonderfully well and refuse to participate in her bad behavior. Trust me, people will notice.
Practice these phrases:
"I'm sorry, I was concentrating on something else. What did you say?"
"I know, sometimes this job can be so frustrating."
"I guess I just didn't explain this well enough - would you like to go over it again?"
"I wish I could be more help to you - maybe you should ask (fill in the blank)."
Not only will this work, you'll get the satisfaction of being righteous and devious at the same time. What a feeling!