I've read through the PM/Bridge compatibility settings and I think I've got them working right. However, not only does setting a picture as a reject in Bridge not transfer over to PM, it makes setting labels and ratings after that very erratic in both programs. After doing it, sometimes I can't change the color label in PM, and star ratings in PM don't travel to Bridge anymore. The only cure seems to be to delete IPTC/XMP metadata in PM and start over.
I know the answer is, "Don't do that!" with respect to rejecting a photo in Bridge. This was motivated by seeing where Adobe seems to store the Reject tag. It looks like they set the Rating of the photo in the IPTC record (according to Exiftool) to -1. Any chance of having PM read/write a Rating of -1 correctly as a reject? If that is indeed where Bridge stores this info...