Interesting... I'm going to guess wildly here. Please let me know if I'm not totally wrong.
I suppose you are interested in her just because you find her exotic? If this is the case, you must come from a "better" family (higher income, education, less drama, etc), and you are probably bored with people of the same "kind". You are now looking after someone "across the border" so to speak.
She on the other hand is dating "bad boys" because that is what she is used to, and she identifies herself with that kind of people, since her entire family is bad. She is looking for guys within her social circle, and that is where your problem lies. You are not her kind...
You have three options here. One is to forget about her alltogether. I suppose you don't like that one. The second option is to become one of her "kind". I wouldn't recommend that either. The third option depends on whether she wants a better life or not, if she is willing to become "your kind" so to speak, and if there is even the smallest chance that she is capable of doing it.
What you need to do is to invite her to "your kind of people" and make her comfortable in their presence. At the same time, try to show her things that you maybe think are common, but that she might find exotic, new and interesting. It is important that she always feel safe around you, and that you provide her with new sensations. Don't hit on her, don't try anything unless it is obvious that she wants it. Just be her friend. The only sexual thing you should work on is your vibe. Watch Julien's PIMP videos at rsdnation, and you will know what I mean. There is a risk with all this - that she will feel uncomfortable and run back to where she feels at home. If so, the game is lost.
If you spend enough time together, and you succeed in introducing her to a better social circle and better life, there is a chance that she will fall for you. And as a final touch to this all - I say all this because I once was in this exact situation myself, with a mentally broken girl in my bed.