How should I approach this girl that I like?

There is this girl who I have a crush on, and I'm trying to figure out if she likes me or not.

We are both freshmen in college, both aviation students. We like a lot of the same music, TV shows, etc. (in addition to the aviation).

I've held doors open for her several times - and she's been saying thank you every time. The most recent time I did that, there was nobody around and she looked/smiled at me in such a way that she seemed really flattered. She has been looking right at me other times, in such a way that she looks like she wants to talk to me.

On Sunday, I was walking out of an elevator and to my surprise she was there waiting to get on the same elevator I was getting off of. She was wearing a sweatshirt/sweatpants and was bringing a bag of chips. It was especially a surprise to see her because she lives one floor above, and people almost always take the stairs. But anyway, I was looking at her about to smile, maybe say something...she looked at me for a second and then looked down.

Was that nervousness? Shyness?

Recently she's been tweeting about relationships/guys...more specifically she's sick of guys hitting on her, she will come to you if she wants something...also that if you never tie yourself down in a relationship you won't be hurt.

Again I've never really talked to her. I'd be willing to ask "how's it goin" if the time was right. I just don't know when I would have the opportunity. I also worry that she would not be interested in even small talk like that, or just see that as nothing more than the question I asked her (by that I mean not developing that into a conversation). I would try to talk to her online or something, but she doesn't really like that and I would feel awkward doing that.

Any suggestions? Thanks for the help.
How should I approach this girl that I like?
Add Opinion