What would you do if you met this girl?

So there's this girl that's been in most classes with me since Elementary school. I want to try and be friends with her and I want to see what you all would do if you met her. She seems really shy and I have never heard her speak once. She always sleeps in class and sometimes comes to school in PJ's or baggy clothing and she never does what the teacher tells her to. I noticed she sits alone at her own table at lunch and eats cookies and french fries a lot. Though she doesn't speak she protects people in school from bullies a lot and helps people when they get hurt or stops them from getting hurt. She seems to get tense around crowds of people to. There's also this German Shepherd that walks her to and from school everyday. When shes mad she bites to, hard enough to make you bleed and that got her the name 'Lone Wolf' at are school. But I catch her crying silently sometimes in class to. Overall I don't think she has any friends at all and I want to try. So what would you do?