Okay, so here's Step 2.
Next time there's a session, is it possible for you to stay behind? Like the other one or two students leave, but you stay behind, on the pretext of asking a question.
Now, this question should be on a topic that you've read up on. Ask something in-depth, and intelligent. When she answers, do the whole stare-and-smile routine again, but this time at close quarters obviously, and remember to stare into her eyes.
Remember to also pay attention to what she's saying, so you're able to ask follow-up questions.
Tell me if this isn't possible.