You don't have any files "in" Adobe Bridge, none at all.
Bridge is nothing more than a file browser, it just allows you to see your images wherever you put them in the Mac Finder.
Whatever you do in the Finder is instantly reflected in Bridge and viceversa.
Bridge does not open, edit, manipulate or even close or save files. It simple hands the files to the appropriate application, whether that be Photoshop, Adobe Camera Raw, Illustrator, Acrobat, InDesign or even MS Word or Excel.
Back up your files in the Finder, using your preferred method do backup files.