What's the Best Way to Pursue a Shy Girl?

Yeah, I'm seeking more advice because I'm about as decisive as George McClellan with an advantage to press. I really want to at least befriend this very pretty girl I met at orientation a while back, but she seems very shy. Though she seems like a nice person from my limited experience, she has a very small circle of friends(her roommate and suitemates, 3 in all). I'm afraid that chasing her too hard will spook her into withdrawing herself entirely, but at the same time doubt she'd take the initiative herself if she wants a relationship(thus effectively putting the impetus on my indecisive, overthinking, still-pained shoulders), due to factors I believe I understand all too well. Any tips?