The only way to guarantee that you won't be watched is to shoot on private property, but you need permission beforehand.
Central Park has a lot of people during the summer, so you will encounter passersby. They might glance in your direction, but they generally don't hang around too long. There are parts of the park that are less crowded than others, but you will not really have a private shoot.
Bryant Park is a public park. See: http://www.nycgovparks.org/parks/bryantpark
Like Central Park, it is also a crowded park during the summer, and there are many events held there, which would prevent you from doing a photoshoot there.
If there is only one person with a camera and a small group of cosplayers (2-3), you should not get questioned by park security. If the group is too large, security officials may think it is a commercial shoot, and that is when you get chased away (because you didn't have a permit).
I was pointed to this link about what photography is allowed in NYC: