I asked out a girl I was friends with at university (she said no). Now we are in the same class again. What should I do?

I met a girl during my classes a few years ago and we spent a LOT of time studying together. Before the semester ended I decided to ask her on a “date” because I thought there was something and I didn’t want to miss that chance. Problem was she actually never saw it coming (I guess she felt 0 attraction AND I never tried to give her any “hints” because I’ve never done that before and would be awkward as hell, so ironically, just asking her out was “easier” for me). She said no, and she was actually getting back with her ex anyway (I didn’t know this).

Later we had a conversation and I asked her if we could still be friends and she seemed happy about it. That was a relief because I wanted us to stay in touch.

The semester ended and we lost contact until the next one started. We shared a couple of classes again. I said ‘Hi’ and initiated a bit of small talk when we made eye contact but I could never overcome the awkwardness to talk to her like I did before, and my confidence was (and still is) close to zero. In general, whenever I lose contact with someone I just can’t break the ice again.

She texted me a couple of times about the finals after that semester ended, then we lost contact again for more than a year.

Now we are in the same class again but I don’t know what to do. Being in the same class every day and not saying at least ‘Hey’ once makes me feel bad. But honestly I’m not feeling confident to do that in front of her new friends. Also, I think part of me still wants to experience that old feeling of hopefulness I had before I asked her out (I know I should forget about it).

I want to decide if I should at least text her to break the ice and see where it leads, or just ignore her forever unless we make eye contact again (I know we probably will be in the same class in the future).

I don’t intend to attract her, but just to make things less awkward for me and (maybe) get back that friendship.

What should I do?

**TL;DR**:

Met a girl. We spent a lot of time studying together.

I asked her out (she said No). We agreed to remain friends.

I couldn’t overcome my awkwardness and my low confidence, so I kinda avoided sitting next to her and just said ‘Hi’ when we made eye contact. Then we lost contact for more than a year.

Now we are in the same class again but she doesn’t know yet.

Should I break the ice, or just ignore her until it’s impossible to do so?

I don’t intend to attract her, but just to make things less awkward for me and maybe get back that friendship.

Thanks to anyone reading this wall of text.