Cinema has what they call absolute texture paths and relative texture paths. If you say "Yes" when prompted to copy a bitmap to the scene location then Cinema creates a relative path, meaning that the program will only look for the bitmap in the local texture directory for the file (e.g., c:\myscene\tex\mybitmap.tif). If you haven't saved the file yet, then Cinema copies the bitmap to the tex folder in Cinema's appdata folder. If you say "No" when prompted to copy the bitmap, Cinema creates an absolute path and it will look for the bitmap in it's current location.
You can convert all your absolute paths to relative paths by using the "save project" command. In that case Cinema will collect all the bitmaps used in your scene and copy them to a "tex" folder inside the project folder.
You can also use preferences>files>texture paths to specify specific directories for Cinema to search when it can't find a bitmap.
It kind of worked...I saved the project and I see it copied all the textures over to a folder. I re-opened the project and it renders out fine...the problem is that when I copy everything and open a new project, about a dozen textures are missing- even though they're in the folder...