I really like this girl but I dont have any idea about what i should do.?

OK, so I really like this girl in my Biology cl. I usally never get shy or scared arround girls, **** talking to most of them is the easiest thing ever. Im one of the more flamboyant people in the cl, on the basketball team, really popular, good looking etc.... She however, is extremely quiet in cl to the point that i dont think ive ever heard her say a word, shes really shy, and doesnt seem to have any friends at school although she is absolutely gorgeous. The sad part is that she sits one desk across from me in cl and i dont know what to do to get a convo going. I could try asking for whiteout, a pencil, eraser or something but then i have like 4 of my friends on either side of me who it would seem logical for me to ask first. Ive never really had problems approaching most girls and i get tons of girls (mainly the loud popular abnoxious ones. you know, the stereotypical cheer leader types) but i dont know how to even initiate a conversation with this quiet shy friendless girl. Anyone with ideas?