Colour labels from Lightroom are displayed incorrectly in Bridge

Hello, one could make the request for the opposite : to have a setting in Bridge preferences that matches Lightroom's, for the many users that use both apps together, with a prevalence on Lr.

As I recall, the colors and/or names for labels in LRC and Bridge were not intended to match. Thus, unless otherwise stated, any matching is purely unintentional. 

But, as I've stated in the past, Bridge and Lightroom Classic should be used in parallel, not in unison. Bridge is a "happy-go-lucky" kind of program. It doesn't care what kind of files are in a folder; it doesn't care if you move files around in Bridge or Finder/Explorer; it doesn't care where or how you made any adjustments.

Lightroom Classic, on the other hand, is a very picky application. If you move a file or change a file's name, it will act as if you threw the file out, and you have to relocate the file for LRC manually. If you adjust a file outside of LRC knowledge, the next time you open it in LRC, LRC will let you know that it was changed OUTSIDE of LRC — who do you believe?

But overall, there's very, very little that can be done in either that can't be done in the other. There's no real reason to run the files through Bridge if you want the images to end up in LRC and Vise Versa. And, to return this back to the initial question, from what I understand, it would require a lot of programming to make the two applications properly share labels. So, it will not be soon for this to be corrected. Any benefit that you might have by running the images through Bridge before installing them into LRC might be made moot.