With shy girls I just try going a bit more low key... almost as if I'm a bit shy myself (and I was really shy when I was younger, so it's not that hard to get in touch with that part of myself). Maybe bump into her "by mistake" and then notice something about her... "Hey, that's a cool pen/eraser/ruler/whatever, where did you get that?". Then follow with a personal story like "I'm always in a hurry when buying my school gear so I end up getting... well pens that are not as cool as yours". "Hm, perhaps I'll steal it when you aren't paying attention.." *teasing smile*. Basically.. make her notice you, make a spontaneous comment (or at least one that seems spontaneous) and make her smile. That's what I would do for an approach, anyways
And remember that with shy girls it's usually more dangerous to move too fast than too slow... don't scare her away when you get the game going. Shy people aren't used to getting good connections with other people, so if you give her that feeling accompanied by a flirty vibe she'll probably fall for you 