After your cold approach (after saying "Hey I thought you really really cute and had to come meet you, hi I'm X, etc. ")
"what are you up to today"
This question can unlock a trillion possible conversation paths. Quick examples off my head:
Me: What are you up to today?
Her: Oh, just picking up food for dinner tonight.
Me: Oh yeah, that's an interesting item you're getting. You must be cooking something exotic...
Her: Haha, no. Just spaghetti.
Me: Oh really? I've never used that before in spaghetti. What kind of flavor does it give it.
Her: *talks about the taste*
Me: Damn. You must be a food connoisseur...
From there I would launch into different types of foods she cooks then eventually try to shift the conversation to saying "we should get together soon. We'll pick a new food recipe together and whip something up".
Me: What are you up to today?
Her: Heading to the library to study
Me: Oh really? Big test coming up?
Her: No. Just writing an essay for microbiology
me: That's interesting. pre-med student?
Her: Yes!
Me: Knew it

What's the big dream after school? Are you trying to become a family doctor, or do you eventually want to travel overseas to help those in need with your medical expertise.
Her: I actually want to be X. But I would love to travel overseas eventually..
From there, I would ponder where she wants to go overseas, and eventually say " I have to head off now but you're really fun to talk to. Let's trade cells and we'll grab a bite to eat sometime".
It takes practice, but you eventually learn to feed off little things in conversations and branch them into a new topic. Granted, as you know I'm fairly new to this too, but I've been getting semi-decent results so far, so I feel comfortable sharing these examples.
Bob