Do not get involved in "proving he is a jerk" but focus on her alone. Call her on the phone and tell her you are interested in going to a movie or other activity with her. My wife was engaged when I met her. I won the prize for being bold.
You pass on this girl cos she's already taken. She won't appreciate anything you do to get in between her & her bf. There's PLENTY of single girls who'd just LOVE to date you, & there's more than 1 girl in the world for you. How would YOU feel if some guy kept trying to push his way into a relationship you had going? It wouldn't be right if they did it to you & wouldn't be right if YOU did it to them.
Well, women that are attracted to total "waste" usually have a plethora of problems of their own. Given a good guy and a bad guy, they gravitate towards the bad. You may wish to set your sights on someone who would appreciate you... Unless you are the type to want what you can't have and that is another issue altogether.