Props for approaching man, but it seems like you really kept with fluff talk. If I were you I would have started with something like(off the top of my head):
Muse: Hey you're in ___ class with me!
Her: Yeah
M: Studying all by yourself right after class huh? I bet you're a total overachiever?
H: blah blah(qualifying)
M: Well you're making me look bad with all that studying! I gotta get outta here in 5 because I'm meeting up with my buddies, but you look like you could use a quick study break. (Sits down, run a routine probably some opinion opener and stack a routine or two. Get into a quick DHV story, and throw a neg in if it's necessary.)
H: blah blah blah
M: Alright, well I'm glad we finally met. I've been trying to meet some cool new people. Play your cards right and you just might make my "cool list"!
H: Oh really? blah blah chick crap blah blah
M: (some stupid #close such as): Hey I've got to get going but you seem really on top of this class, I'm doing well too, but I always study better with a partner. We should meet up and study together for the next exam over coffee. *hands pen and paper*
H: Oh cool yeah that would be great! blah blah
M: Yeah, you and me, we'll be the dream team. We'll set the curve, haha. Alright well I've gotta get going. See you soon.
H: Ok, Byyyyyyeee (leave with a hug)
It's just off the top of my head and I know I can do better, but it would be a quick way to get a number close out of it. Also it's definitely more interesting than talking to her about class the whole time

. Gives you a chance to show some real personality rather than just fluff talk right off the bat. Keep it up with her, even though you didn't number close right away it's totally salvageable at this point I believe. I generally take it slowly with classmates, unless of course I meet them outside class!
Hope this helps.
~Muse