Like you mentioned, some do and some don't. For the sake of everyone, we'll ignore GWCs (guys with cameras) who just want to shoot girls for their own "personal reasons."
One is to determine the right place to ask. Asking on Craig's list or a place where people are seeking jobs is a big no-no. Start asking around in communities like OMP (One Model Place) or MM (Model Mayhem), where there are people developing their portfolios. Or as a photography school, art college, or art department, as student photographers are more than willing.
As far as what determines if a photographer will shoot trade, generally a good look that appeals to the photographer, an experienced model that knows what they're doing and/or has been previously published, a model that's willing to try out new ideas, or a model that's willing to go the extra mile (shoot in the early morning, in the cold, or literally in locations further away).
Sometimes a model that doesn't have an existing portfolio isn't appealing. You may want to consider hiring a photographer once to get you started.
Also, a model that only has retouched work posted generally is a sign that you might be hiding a scar, tattoo, or bad skin. You want to let photographers know about those things, as well as measurements and such.
Sometimes a compelling idea will draw in a photographer, so don't be afraid to suggest a concept. Preferably not something they've previously shot, as that doesn't add to the photographer's portfolio.