I wish I had an answer to this. If I did..., I'd definetly, upgrade from Bento to Filemaker, if it could be made to work without re-importing every media file.
However, if you open the Bento.db container via the Finder by right-clicking and then select Show Package Contents. In the new Finder window find Contents/Resources/Assets for image files (in my Bento.db anyway). I suspect that other media files might be hidden in the Contents/Resources/Media folder. You can manipuate those files and folders independent of the Bento.db (copy, move, edit, cut, paste, etc.) so, perhaps someone could figure out where to move those folders or files to within a FM database while maintaining the links with your records. I reckon that's the tricky part.
That's about as far as my guess goes.