I am an over analyzer as well, and not the quickest on my feet either. However, since I've been doing this now for years and years, I have developed a sort of microfiche cheat sheet in my mind...certain answers for certain questions and situations...that make me appear to be very witty indeed. Takes time to compile tho, but basically anytime a woman had stumped me or 'got my goat' in the moment, after the fact I would think about what I SHOULD have quickly retorted with. Then, I store THAT response in the database. Then what would usually happen is once I finally got the chance to use it, her retort would be another stumper so it's back to the drawing board!
As far as your situation...so many ways to skin this cat. She may eventually...or she may not. Girls at this age have so many options to choose from that she really doesn't HAVE to do anything. If you don't feel like waiting and can tell that she does indeed like what she sees, then approach her short and sweet. Be like, "Hey, I'd like to talk to you, but whenever I do see you, you are always with company. Here's my number...I look forward to your call."...then WALK AWAY like you have a pressing matter to attend to. Then, it's on her....but if your read is correct, and there is nothing else going on in her life that would make calling you a tough decision, she will call.
Or, since school is a long term environment, start by speaking to her everytime you see her...just a simple "Hi...how are you?" will suffice in passing. Do this for a couple weeks...hopefully the convo will gradually get longer and a little more substantial. Then one day when you see her, walk where you KNOW she will see you, but pretend you were in a hurry or otherwise preoccupied. If she calls out to you, you are in there like swimwear. If not, doesn't mean it's over...just depends how much effort you are willing to put in versus whatever else she has going on in her life that she feels takes precedence over you.
Good luck!
_________________
EVERYTHING in life is conditional...
EVERYTHING.
Pimposophy Revisited is now finally available on Amazon in all territories!