I was expecting she would bear the evidence of her death like the ghosts in The Sixth Sense or something and it would be really creepy but she just looked like she did when she was alive. Early 2000's punk/goth girl, rocking a Hot Topic corset top, kind of witchy silver jewelry, dyed black hair with blue streaks, heavy black eyeliner, etc. (I found out later that she had been dressed up for a date when she died.) Kind of Too Cool For Me in both appearance and temperament, but once I expressed a desire to help her she started to become more friendly. All the previous occupants of the room tended to leave screaming as soon as they knew the place was haunted, so she had given up on trying to communicate some years ago and just amused herself doing ghosty things. Her name was Morgan, and I feel like I knew her last name too because I ended up having to look her up in the school database but I don't remember what it was now.
She revealed that she had not, as was officially believed, committed suicide, but that she had been most treacherously murdered by a professor she had been illicitly dating. The relationship had been taking a downward turn, they got in an argument, and she threatened to reveal their affair, so he killed her. She was disgusted to find out that the same professor was still teaching there, and probably still taking advantage of students. So we devised a plan to get revenge on him by tanking his career and exposing his misdeeds to everyone. I don't remember all the details now, but it went on for several weeks of dream time, during which our friendship evolved into casual flirting, and with a vague sense of both joy and despair I realized I was falling in love with a ghost.
I miss her now that I'm awake. I have dreams like this every so often. It's always a different setting and scenario with its own story, and we're always meeting for the first time. She tends to look a little different every time and have a different name, but after meeting her I always have this spark of soul-deep recognition. Oh, it's you! Maybe somewhere in some world there's someone else, dreaming of meeting me?
At any rate I have this accumulated stockpile of dreamed meet-cute (or meet-weird) scenarios that would make good story/comic leads if I ever had time to write them. ;)