I [18/M] just met a girl [18/F] and I'd like to get to know her better

I'm a college freshman, and today was the first day I had one of my classes due to switching and stuff, and I saw this girl who I thought was cute. I remembered I saw her in my previous class, so I introduced myself and we ended up being lab partners in the next class. We talked mostly about the work, but I asked her about what she does and stuff. From what I could gather, she's similar to me in that she commutes, focuses on her work and seems to have some interests in the same fields. I think she'd be a good friend, but I literally met her today, I felt like it would be weird if I asked her for her number or anything. I asked to hang out with her but I realized I was almost late to my next class, and tbh she didn't seem crazy interested in it. I'm pretty sure we're going to sit next to each other again next week cause the teacher asked everyone to stay in the same seat, so I might get another shot then.

Is that a bad thing? Or should I just wait till next time when we have the same classes again and just talk to her there and see if I can hangout or something?

I'm kinda shy, so college is crazy to me and I'm trying to open up to other people.

TL;DR: Acquaintances, didn't talk crazy much but she didn't seem to hate me or love me or whatever. How can I go about trying to get to know her better, as I'm just trying to make new friends and she seems pretty nice and easy to get to know.

I feel like I'm going a bit overboard with this, I just kinda feel like I fucked up not asking for her number or something.