How do I induce this girl to become friends?

there has been a girl on my class,(apart from myself) ,who was the only one to speak up against the class bully.she's not new or anything .we have been on cordial terms but not friends.we share interest in books and music too.

how should I induce her to become friends .she moves in a group of girls that hate me 4 being introverted and will try their best to dissuade her from being friends with me - as thesegirls have to many other girls who could become my good friends.How do I induce this girl to become friends?
when no others around , walk to her, chat with here friendly,if you willing, you will be good friends,How do I induce this girl to become friends?
I would talk about music and If that dosent work then you can talk about books and if you guys have nothing in common besides that and she shows no intrest then I guess you guys werent ment to be friends
Friends kinda just happen, there isn't a way to get them to be friends if they don't want to be or if they have people influencing them . All you can do is when you see she is reading something you like and have read too, compliment her and strike up a conversation, try talking about your favorite part and see if she likes it too. Ask for her opinion of something ( make sure it isn't shallow like ';do you like my outfit '; because that could backfire on you) try like , ';Do you like the way our teacher Mr. / Mrs. ______ talked about .......';