Short of her brining it back on her own there is no method except the police. If she gets into an accident it is common for the car owner to be included in the lawsuit. Here is the more interesting question you face, is she an excluded driver on your car insurance policy? Not only may you be liable but depending on what happens the insurance company may or may not be required to insure the loss.
I am an Arizona attorney. AVVO does not pay us for our responses. Simply because I responded to your question does not mean I am your attorney. In Arizona a non-lawyer is held to the same standards as an attorney so there are dangers to representing yourself. This is for informational purposes only and should not be considered as legal advice. If you require legal assistance an in depth discussion of your case is needed as there are many other issues to consider such as defenses, statute of limitations, etc.
My goodness -- I know you do not want charges to be pressed, but without law enforcement involved, there is no other remedy.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
Based on your post, you kicked her out, she is not going to bring the car back. You are potentially at risk if there is an accident and she is at fault.
The only smart thing i to report the car as stolen and provide as much information as possible re its whereabouts and the circumstances relating to how it got there. If you just say stolen, some DA might decide you were trying to commit a fraud.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.