Thank you. Unfortunately, there probably isn't any legal action that an individual in your circumstance can take. Name calling is impolite and unprofessional, but not illegal. Making factual untrue statements can give rise to a claim for defamation, but you would need to link this employee's statements to a financial loss of some kind in order to have a claim, and unless you are fired or demoted because of the statements you don't have that. Furthermore, you would have the burden of proving that the statements were false, and it's almost impossible to prove that you "aren't a liar." The "bullying" statement is a statement of opinion, not an objective statement of fact and so can never give rise to a defamation claim.
Then, on top of all, this, the best case result of a defamation suit is a judgment that will most likely be uncollectable because this employee won't have the assets to pay it. Really for all these reasons, defamation actions against individuals are almost never practical to bring.
So, as a practical matter, all you can do is continue to document this employee's offensive and unprofessional behavior and "build a case" so to speak so that your boss will give you the authority to take the disciplinary action you believe is appropriate. As her manager, you should already have this authority but some employers like to keep a tight grasp on hiring and firing authority and so situations like these are not unheard of. Basically, you need to deal with the situation on an interpersonal level, being mindful of the company politics at play. Regretfully, the law is not going to be much help to you here.
If I can clarify anything at all for you, please do not hesitate to ask. It is my pleasure to assist you further if necessary....