Adobe Bridge is an organizational program created and released by Adobe Systems as a part of the Adobe Creative Suite. Its primary purpose is to link the parts of the Creative Suite together using a format similar to the file browser found in previous versions of Adobe Photoshop.
It is accessible from all other components of the Creative Suite (except for the standalone version of Adobe Acrobat).
BRIDGESORT is a file cabinet system file used by Adobe Bridge software to dictate how photo files are sorted when viewed in Adobe Bridge (i.e., name, date, extension, etc.). Normally this is a hidden file and can be safely deleted (but sorting will resort to the default in Adobe Bridge next time you view the folder in Adobe Bridge and a new version of .BRIDGESORT will be then created).