Did she even go to that school? They ran into her at the university.
After killing that guy who was about to turn, she stole a car (end of ch54). She left the university, because she's "gotten bored of these gloomy expressions" (read: people). After driving around and feeling special for a while, the car broke down with a loud bang, trying to restart it only had the engines gurgle and she was quickly surrounded by zombies.
From the text it's unclear where she was heading, but she knew about the main group, was around when they were interviewed about their past, learned about the aerial infection and rumors about a cure, in connection with our main characters... So, maybe when she got infected, as she was trying to escape the car, in her frenzied state ("But... I'm choooooseeeen!") she made a false-but-right connection and went to the school, looking for an antidote / cure against the virus, turning on the way and her last coherent thought kept her on her path and stuck around the school.
...but, yeah, I had to go back and read up on several chapters again to piece that together. From her character and what we know she knew, I'd say my narrative is a good bet. But just like the main characters, we'll probably never know for sure..
...Oh, and I finally found her name. Ayaka.