This might sound irrelevant but today’s time is not about trusting strangers, you must not trust someone you don’t know and always keep alert whenever you get in between such people. The girl who asked you for the lift was a complete stranger to you and she took her chance on you to blackmail you. This kind of blackmail comes under extortion in which a criminal or fraudster asks or demands money in exchange of keep their mouth shut for not relieving such kind of things. 
 
What you can do?
You can look for legal support and file a zero case where you can say that if anything happens to you it will be the lady (who blackmailed you) fault and responsibility. File a case against her and ask the cops to take strict actions to save your reputation. If a girl alleges and accuses you of attempting rape on her, you can ask the police to do a medical investigation of the girl. This way they will know if she was forced to make sexual intercourse with you forcefully. 
 
What do you need to keep in mind while filing a case against her?
You must keep some points in mind as you also need to keep yourself on the safe side:
 
Make sure she doesn’t have any sort of fake proof against you as there might be chances she had planned the whole scenario in advance.
You must take care that you’re going to the police with full preparations and you will not step back and fight until the end. 
Your site must be clear and free of any doubt because the police will try to put you in a girl’s shoes and that’s where there would be chances that you’ll be imprisoned.