Can you sit next to her and naturally start a conversation? If you could do that for a week, then ask her for coffee (and I wouldn’t even think of it as a coffee"date" just having coffee with a classmate), then you could get a vibe from her. That would be less risk. But “Hey do you want to get a cup of coffee after class?” Is fine too. I might make a comment about the class or her input. “Can’t believe we have to read ten books by Friday.” “That was funny/smart/great what you said.”