Starting a relationship help?

I have a cl with a girl I really like...But I haven't the slightest clue how to go about initiating any form of relationship with her. The only reason I'm even in the cl is because I failed it the previous time around and had to retake it the next year. Shes in 9th grade, I'm in 10th. Its an English cl, and typically that is the only time I see her during the day, so there isn't really ever any opportunity or viable reason for me to initiate a conversation with her. I sit next to her in cl, and she seems shy or nervous. Mumbles kinda when she speaks, cracking fingers, wringing hands, tapping pencil. But oddly enough at the same time her personality seems expressive. The most I've talked to her was when I offered her a piece of paper, or when I asked her what time our cl ended (fail, blatant conversation starting attempt.) Shes obviously intelligent, awesome personality, extremely attractive. Lastly, she has a facebook...Would a person in my situation adding her for no reason have positive effects, or would it seem creepy? I really like her and would hate to see this semester end and only see her around occasionally, aka no chance for an anything. my primary motives for a relationship are purely based on the emotional aspect, I'm not some @ss who thinks shes pretty and wants to get laid. Entirely love based, any help is much appreciated.