Bibble uses a specialized XMP file to handle things like supporting multiple version of the image, according to their web site. (I've been using Bibble much longer than I've used Photo Mechanic.)
The Bibble-proprietary XMP files do contain the ratings information (in an old, successful, directory). I don't recall that I've ever experimented to see if changes made in Bibble propagate back to being visible in PM; it seems unlikely on the face of it, but I don't care. For me PM is very specifically for the initial big sort of everything at once, and I don't go back to use it again later on the same photos.
I'm well aware it's not you job to support Bibble here; I started here because I observed a change on two systems when I upgraded PM (and didn't upgrade or reconfigure Bibble in either case), which makes me think in terms of something having changed in PM.
I had a fuss getting things to communicate the first time around, but I resolved that, and have been using it happily for months (being able to eliminate a workaround I used for a while requiring moving the photos at each level into separate directories). In the short run I can go back to the workaround, but that's really very undesirable in the long run.