I used to always find these girls to be anti social as all hell, but think of it this way.
Does the girl sitting alone at a table in the cafeteria reading a book/doing homework not want to be spoken to? If you watch closely, she'll often look up to see if anyone might be thinking about sitting down with her. I've interrupted and felt like I was being very bothersome to many girls who were doing homework, and it turns out they are starved for conversation.
I mean if they really had to do homework, they'd be at their house, alone, locked in a room. Or at the library in one of those "quiet rooms". She's just passing time and you can help her pass the time.
Think of your voice as the new soundtrack to her day. She may enjoy whatever music she's listening to, but she could just as equally enjoy your voice.