Hi Doug,
Probably not from a previously rendered .bmp file.
I'm not sure how the folder name is determined for "temporary output files" and if that might be of use in determining the render project file.
The best way would be to include the render variables ${TGDNAME} in the name of the output file when rendering.
I image it might be possible to write a script that would parse the TGD files within a folder structure and let you know the output file paths.