The idea of using both Lightroom and Bridge just means extra work for you. You'd be better off applying keywords in Lightroom than doing it in Bridge and then synchronizing to Lightroom. Then this problem of the synchronizing being slow goes away.
The issue is that by default LR stores all metadata in the catalog file and not in the image file or XMP sidecar. To work in both LR and Bridge the metadata must be manually updated (read) from inside LR after any metadata changes in Bridge. For Bridge to see metadata changes made in LR you must "save" the changes from inside LR.
Comment synchroniser les mots clés et note de Bridge? Je veux travailler en Bridge, puis synchroniser pour avoir les mots clés sur le disque.
Mais c'est tres lent, et marqué 'incompatible'. ou 'conflit'.
To update your Bridge metadata changes inside LR select all of the updated files and go to menu Library> Metadata> Read Metadata from File. Be aware that any metadata changes (keywords, ratings, color, flags, etc.) made in LR will be lost and over-written with the metadata showing in Bridge. To prevent this from happening in the future you must update the image files after every metadata change inside LR by selecting all edited files and using menu Library> Metadata> Save Metadata fo File (CTRL + S). To do this "automatically" check Catalog Settings> Metadata> Automatically write changes into XMP. The links Mohit Goyal provided explain this in more detail.
You can use the LR Filter bar to find files with metadata conflicts. Select 'All Photographs' under Catalog in the Library module and the below filter. If you know that metadata was only entered in Bridge then it is safe to select menu Library> Metadata> Read Metadata from File.