You don't need a whole short story or anything. In fact I'm a big fan of brevity when folks can manage to do so and still convey a strong sense of a character, what their motivations are, how they might respond to certain situations. A few paragraphs would suffice.
This is not what I'm requiring or anything, but occasionally when I'm trying to think through some characterization I'll go to the 10 minute background to get some good bullet points for my character, some quirks, and how they relate to their world. You could always try that to get yourself started, then flesh it out over the next week a bit before you submit.
I've also been intending to add a small piece of intro narrative, to set the scene before play begins. Looks out for that as well, maybe it'll give you something to react to.