If this is serious you could, the next time you find yourself chatting with her in a one on one scenario that feels natural, ask her if she wants to grab coffee or lunch or whatever after class sometime If she says yes approach that as if it is exactly that; a coffee or a lunch or whatever and nothing else and go from there. If she says no then you say no worries, see you next class and you move on and that's that. You tried and you were cool about it and everyone just goes on with their life and it's all fine.

I think generally it's extremely difficult to just ... Talk to people. But that's usually okay to do especially in this kinda scenario. Asking once, gently and in a safe place that she can clearly say no one and not being weird about it is fine. It's not taking no for an answer or making it coerced or with strings or being weird about it that becomes the real problem. Or it's like obsessively not asking but instead staring or approaching weirdly or acting as if she owes you something that it becomes an issue.

And if this is a bit then I missed it which happens oops.