does this person want to hangout out

I met someone in class who I could see as potentially a friend. We didn't talk much because it wasn't a class where you talk a lot (which is good but yeah lol). I added her on facebook and she accepted. We talked and she said that I was nice too. I realized she was on a trip so I asked her if she wanted to hangout (so she would feel free to say no or not). She said she definitely wanted to hangout when she came back and got used to the time difference. It's been two weeks and she told me she's back and how I am doing. Should I ask her to hang out again or should she if she wanted to? I don't want to seem desperate for a friend lol...

I think you are on the right track.

Its ok to ask every now and then if you may spend time with her.

However, I would avoid pestering her about it. She might attain a misconception that you are a stalker.

I think friendships/relationships are like taking turns on a one-player videogame. She gets a turn and you get a turn; in this case, its taking turns asking if and where so-and-so wants to hangout.