I don't know how ASP does it's session handling, but having them pass you a userid would work. But then your program wouldn't have any security since anyone could send you a userid and a spoofed header and have access to that users information on your system.
Since I don't know anything about ASP I can't be of much help in trying to figure this out for you. You should get together with the developer of the ASP system and see what you can come up with together.