You remind me of me when I was in high school and early part of college. A shy, nice boy/man who is scared to death about making a move on a girl. Even when all the signs are there and she's waving the flag in your face, you are unsure and hesitant. I learned to overcome this fear over time, through experience.
Your problem stems from a mis-conception that all girls are good and that you have to treat them like your 6 year old niece. You cannot conceive that a girl just wants to bang (or screw) for lack of a better/appropriate word. That right there is your main problem. You were afraid to make a move because of what might happen if it fails. You blew it big-time, that is correct. What you should have done is pulled the car over on the side of the road and did it right there in the backseat of the car.
I have good news for you though. You may still be able to salvage this girl. Just because she's dating someone or is "in a relationship on facebook" means very little. If she's still into you, then she may be willing to give you another chance. You have to make the first move though. Maybe facebook friend her and chat casually. Try to set up a date, or just hang out (don't call it a date). Also, alcohol works wonders. Sit down with a 12-pack of beer and a good movie. During the movie, guage whether she's interested or not by seeing if she touches you multiple times. If so, you have the green light. Wait until you're both relaxed with a few beers in your system and make your move.
If she isn't receptive to meeting up, then all hope is lost for now. Maybe she'll get in touch with you when she breaks up with the other guy eventually. But you don't want to wait around for that. There are plenty of other girls. You just need to learn from your mistakes and move on.