I don't want to pay for my share of a hotel room I booked with my girlfriend.
Why don't you want to pay for your share of a hotel room you booked with your girlfriend?
She only stayed for one of the three nights that I paid for.
It's fine to not want to pay for something you didn't get.  If you had an agreement that your girlfriend was going to stay in the room and then she didn't stay in it, then she should pay for the room.
I'm going to make her pay for the room because I refuse to pay.
It's frustrating when someone doesn't do what they said they will do. Tell your girlfriend that you booked the room for her and she was supposed to stay three nights. Since she decided to leave and changed her plans, she should agree to pay for the room.