How To Befriend A Shy Girl?

I have talked with this really nice girl but she's shy and I have read a little about how they don't initiate conversations and don't show any signs of liking you or not. I don't really talk to her in person that much, more so online helping her with physics sometimes. I really want to be better friends with her but I am having trouble coming up with a way to initiate a conversation so that she understands that I want to be friends with her. I have no idea what to talk about and I feel as if it would be too random to just asking about her life. Any ideas? It's harder than people say it is, being a shy person myself.
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I'm not a really social person, because I don't do drugs, act immature, or go to parties, I don't really have a popular group of friends. I have some friends but they too are like me. I can't ask anyone to help me out because the people who I would ask would think it's weird coming from a person like me. It's hard to describe my situation but I'm basically by myself on this one. And she is a year older (junior).
How To Befriend A Shy Girl?
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