Thanks for the responses, guys. I'll have the class in two days and try one of these openers.
@Interlude: I realize that the opener I made does come off as semi-needy considering I remember her major out of everyone else in the class. I was trying to tone it back by saying I couldn't remember if it was her or not. Don't know if that really helps.
I think I'd be fine to hold a conversation with her especially with the suggestions above. My biggest problem is the first line to get her drawn into the conversation because I don't have a reason to be talking to her. I'm probably over-thinking it. She's not really talkative, but she is a HB for sure.
I don't know if it makes a big difference, but I was peacocking during our first class. Wearing clothes on top of the current trends, spoke a lot, tried to look as confident as possible. I'm pretty sure 95% of the class had their eyes focused on me. In fact one girl stared at me while I was talking and was still staring after I finished. It seemed pretty obvious she wanted my attention so I looked over at her and we locked eyes for a clear second before she looked away. I'm not interested in her, but I thought it was cool.
EDIT: Okay so I spoke with her today. Without going through all the details, here's what happened. After class was over I approached her and asked if she had the book for the class. The teacher had assigned homework from the book and I don't have it. She ordered the book through the mail and she would get it between tomorrow and Friday. She agreed to let me photocopy it if it comes in before the assignment is due and gave me her email.
The assignment is due to 2 days, so I'm going to email her tomorrow and hopefully she has the book. Though I was getting kind of bad vibes from her though like that she didn't want to give me her email (or number). If she doesn't have the book, I'm going to try being friendly towards her during class and build off of that.