How to ask out girl from my college?

Okay so there is this girl I go to college with that I really want to ask out. I was feeling confident and was about to do it the other day, but then I started overthinking everything and couldn’t bring myself too.

The problem is, is that I have every class with her, so if I get rejected it will make things awkward, and I don’t know how to smoothen it out if things go wrong. Like that will make every interaction between us awkward in the future. Also most of the time I see her, there is someone else with us, either one of my or her friends.

Now we met at the start of college a bit more than 3 weeks ago, and if we talked casually outside class, mostly as a group though (with other class mates). I don’t know her very well, but I though asking out for coffee would be a good way to get to her know her better as its hard to have more than surface conversations when we talk in groups and such. I also don’t even know if she has a boyfriend, I have no clue how to ask that before hand, though it doesn’t seem like she does by the conversations we have had. It’s hard to tell.

Now the reason I was feeling confident is because I began to notice a few things when we talked. She laughs at every joke I make, even though most of them are pretty mid. She also tends to keep her eyes on me when we are in the group. Also if we are sitiing somewhere she always choses the spot right next to me. I think I can be overreading the signs, but in the past this is what I found to be signs.

So, how should I go about asking her out if I should? And any tips for smoothing it over if she isn’t interested?