Getting that fun but distant, popular, nerdy girl? (Ten points!)?

I'm in high school, and I've met this girl. She is absolutely gorgeous and shares pretty much all of my interests. The same instruments, music, TV shows. I mean everything. She's perfect and exactly who I've pictured my dream girl as. I'm a weird person, but this girl is the same kind of weird and she totally completes me. Problem is, a nerdy girl attracts a lot of nerdy guys. She has a lot of guy friends and I fear that it would be hard to win her over, and have her see me as more than her other friends, even if not romantically. Maybe become her best friend and let time develop us into something more. But then again, she is a female human, and it's in her DNA to become smitten and attracted to the right guy. But how? She said she's a distant and independent person outside of school and doesn't really text much, so I'm thinking if I could get close to her she might let me and only me in. Everyone knows the way to get close to someone is by making them feel comfortable to open up to you, and they will become emotionally attached to you. But this girl is a tough nut to crack. I told her that I'm here for her if she ever needs someone, and she said "I don't know how to respond to that" and gave a nervous laugh. Every teenager feels down sometimes and could use a shoulder to lean on, and I want to be that shoulder for her. I really need your guys' help in finding out how I can get this beautiful, perfect person to open up to me and grow attached.

Thanks!