How do you approach a lonely girl?

There's this girl who've I been noticing quite a bit lately. She's almost got a goth thing going on, but she doesn't dress overly weird. She's got beautiful dark hair, gorgeous green eyes, and voluptuous lips. But sadly I've been seeing her pretty much alone and a lot of girls talking trash about her. She's quite smart because I remember going to school with her and she always had like a 4.0 average. I notice she usually rides her bike when its warm out, and like I said, she's by herself. I want to know how do I approach her without her getting nervous (in case if she's anti social)? What things should I bring up when talking to her?