Tough call, and it can really be all over the place.
At the bottom end, you've got a simple TFP/TFCD shoot, where no money changes hands. The acronym is Time For Prints, or Time For CD, meaning that both the photographer and the model benefit by having additional photos for building their portfolio. Many inexperienced photographers and models do this for practice and/or fun. The risk is that you may be working with an inexperienced photographer, and the photos may not turn out as well as you expect. Still, the photographer should be able to show you at least a small portfolio so you can get an idea of their style and skill level.
At the top end, ... well, the sky's the limit, really - especially if you've got an experienced professional photographer who is traveling to you specifically for this shoot.
If you're doing it at a convention, where the photographer who is already going to be there with their gear, and already in the mindset of taking cosplay photos, the rate seems to be around $15 to 30 for a session, resulting in a finished set of six to twelve photos*.
Outside of a convention setting, where the photographer is making a special effort just for you, I'd expect probably $50-200, depending on the photographer's professional experience and skill level, and hoa many different cosplay or variants you want to do in the session.
* the number of finished photos can vary widely. Most experienced photographers and pros will not deliver every shot they take - they'll pick the best shot from each look/pose to process, finish, and deliver. Six to twelve per session is generally enough to cover most of the looks of a particular cosplay, unless you have a lot of props and armor that warrant many detail shots.
As a final thought, I would advise you to practice your poses and facial expressions in a mirror before the shoot, and maybe even bring some reference character images on your phone (or print). Dramatic pose and facial expressions make for interesting photos. An experienced portrait photographer will be able to help you with posing, but they might not know the character.