Photoshoot times vary greatly and I wouldn't suggest to expect any real time. Depending on what you're going for, it can be 30 minutes if everything is in a studio all ready to go for you to the entire day if you plan to hike out to the woods and do an epic shoot with a narrative and other people in the shoot. At cons I do 30 minute slots with the declared expectation of going for 3-6 great shots. Even in an hour long shoot we may only hit 6. But I go for particular shots and you can see the samples in my sig. For my last environmental shoot for a "James Bond" shoot, we spent 6 hours in a parking lot and got two images we were proud to display. I declared from the get go that we were probably only getting two shots, so everyone knew that going in, and everyone LOVED the shots.
For your responsibilities I would highly highly highly suggest getting sample images of your character and saving reference photos of the poses on your smart phone to show the photographer. You don't have to mimic the exact pose or shot by any means, but it's incredibly helpful for the photographer to understand the personality of the character and to get general poses that fit that character. Even if when try to mimic a drawn picture, we end up seeing opportunities to do much more and the final shot diverges so greatly it becomes its own image.
If this is all planned, the photog should preferably be at the location with the lighting all set up for at least the initial shot and should have a few more ideas ready to go. If you guys are meeting up and winging it, expect your shoot time to be 3x normal and not nearly as smooth. You should be partially in costume (especially makeup if you're doing this outside a studio) and be able to get into full costume quickly. Be on time, because if its outdoors, 15 minutes difference can literally mean the entire shoot is undoable. If its a studio rental, 15 minutes can mean big bucks.
As for shyness, there's no real way other than to have a good director and to have the right attitude that you're going in this all out.
I consider myself a very good director for total beginners and one of the biggest things I do, especially with cosplayers, is to really encourage them to "go big." As in , OVER ACT. It's really hard to overact so much in a cosplay shoot that it actually looks awkward. If you're a creepy zombie with her neck dangling, bend your neck will it almost hurts. If you're supposed to be slashing an enemy with a sword, open your mouth and get your rage face on times 300%. It'll barely look "enough" on camera, haha.
Probably the most important rule though is.......just have fun
Nobody looks good when they don't want to be there and hey, you're paying to have a good experience so why ruin your own shoot? Good luck!