First post here, and I'm no PUA so could use some tips.

I'm a sophomore in college. There's this cute girl I kept seeing around I found very attractive, but never got the chance or nerve to talk to her. I saw her sitting down at a table alone a few over from me, and decided to go for it. My AA was the worst its been is years. I've never gone up to a girl I didn't know outside the context of a party.

Anyways, I eventually walk over, and she's writing an essay. I say, "Hey sorry to interrupt your work, but I'm getting some starbucks right now, want to come get some with me?" (starbucks is a minute walk away).

She smiles pretty brightly and says "Sorry, no thanks."

My nerves took over and half-mumbled, "Oh, ok." And walked away.

Overall, I feel pretty good for a rejection, having actually gotten the balls to do that. My good friend who is also friends with her said she probably was too absorbed in her work (finals week is next) to take a break. I'm inclined to agree with it because of how she smiled, but I don't want to overthink it. If there's an opportunity where it would be natural for us to talk, I'll take it, but I won't be approaching her again for now.

Any tips, comments, thoughts?