There are two things here, and the error you get is not the big one!
The big problem is
That that code isn't going to capture the webpage, except on your development machine - C# code runs on the server, not the client, and has no access to the client display.
It "works" on the development machine only because the client and server are the same computer.
The problem you have noticed is probably the Server.MapPath trying to work with a folder that isn't there (the path is relative to the current page , and you probably want:
bitmap.Save(Server.MapPath(@"~\File\ScreenShot.bmp"), ImageFormat.Bmp);
Or the folder does not have the appropriate access permissions set so the folder does not have write permission for the user running the IIS code.