Flirt aggressively, see if she goes for it.

"You look amazing," you blurt out.

She stares at you in shock. "I... well... thanks?"

You take a step forward, putting a hand on the door frame. "I came here to ask if you... you..." Your thoughts go blank but the first thing that comes to mind dribbles out. "...wanted to go to a frat party tonight? With me, I mean."

"You're asking me out?"

"Yes, I mean... you don't have to go. If you don't want to, but I'd love it if you--"

"No," she says, completely regaining her composure. "I'm your R.A. I can't go to a party with you. At worst I'd get fired, at best, I'd lose the respect of everyone on the floor."

Common sense comes back in small doses and you realize your error. That's what you get for letting your dick do the talking, huh?

You bite your lip, thinking as best you can. What could you do?