I know this girl from university since last spring which I found attractive but she was in a relationship then so I didn't advance anything with her. We aren't close friends, but we get along quite well. This semester we shared a course but I still didn't do more than talk and chill with her during the course although she mentioned she had broken up with her bf somewhere in september because a) I wanted to focus on finishing my bachelor and b) I got hurt pretty badly in a situationship in summer and wasn't ready to approach anyone before I felt ready again.

Now although the semester is finished and we havent interacted much since then I started to develope a crush on her and started to slowly text her a few days ago. Nothing much but she always seems to reply pretty quickly.

How do I move this foreard. Ask her to hang out? Ask her for a coffee? Ask her directly on a date?

The goal isnt just to hook up but a real relationship. Im quite inexperienced but Im sick of constantly making excuses why I dont approach women or get a relationship rolling.