This is why everyone says, "Never co-sign on anything with anyone." Now you know why. I just have to make this comment for anyone else reading this. And most people make this mistake only one time.
What state are you in? Some states have some rules on this topic as there are cases when the other owner leaves the county, can't be located, etc. And they may offer some way to transfer the title, but that may require a special process and some bond being posted for the value of the vehicle in case the other person appears and makes a claim to the vehicle.
But really this is a civil matter, for a civil court, ie, if person A says they want sole ownership and person B can not be located.
As others and the DMV have said, you are joint owners, now and that will not change when the loan is paid off. . One thing to note is that you both are joint owners on a vehicle with a lien on it. Does not exactly matter here, but many people think you do not own the vehicle if you have a loan. You do own it, but you do not have the title and can not sell without the lien being released.
Also you have to note that each joint owner has 100% rights to the vehicle, regardless of who makes payments, uses it, washes, etc. So you have to be careful here, she may simply assume she has no rights to the vehicle.
Are you on speaking terms at all? How is her credit? Does she care about her credit?
Best solution. Hire an attorney. They are good at negotiating. Attorney may suggest you call her to prep her atty will be calling or atty may want that bit of surprise....This is an important matter and you need to help get it resolved. Have attorney contact her and say he is working on this issue for you, and inform her this is impacting her credit, if there is an accident she will be involved as an owner, and if you can not pay then she would have to make payments or face a repo and collections action by the lender. Summary - best to get your name off the vehicle.
Atty. would have her sign power of attorney and any state required forms. Then you payoff the loan, borrow the money from anywhere you can. Maybe atty offers her a payment....Tells her if you come in and take care of this right away you will be paid $500 for you time. Of course you are giving the attorney the money.
How much do you owe, what is car worth? If you have positive equity, then sell it to a dealer. Of course she needs to be present. Example you tell her we need to get the car issue cleared up, meet me at dealer X they are going to buy the car and pay you $500 on the spot.
Or you pay chicken with the payments. If she will not cooperate, Tell her you will not be making the payments and that you plan to keep driving the vehicle, but she needs to pay. If she gets mad, then you say, "This is why I offered you the other options and $500 to get out of this deal. You declined, you are responsible to make the payments."
But this will ding your credit, and you can't really let it go to repo status. Which can happen at 60 days past due.