Can you join some extracurricular clubs? I remember there being a lot of those and their purpose is basically to give people a chance to socialize. If there's a subject you like and there's no club for it--you could start one. I started an anime club years ago at my college and I made some good friends that way.

Another possibility would be to start a study group for a given class--you could try for a group for each class you're taking, to broaden the options of meeting people. And you don't have to approach people one-at-a-time. You could just send an email to the class looking for "study partners" or saying you want to start a "study group", etc. Among other things, it would give you something you could say to that girl--"I started a study group, you want to join us?"

I've never done well with "optional" or "free-form" socializing. I do OK at conferences for instance, because I can talk about work with people, but I do poorly at weddings where I have no idea what to talk about. Clubs and study groups give a purpose to the interactions so they might be less stressful/bewildering. This is just my experience.