Dropbox to Bridge

As long as you're talking about the DropBox folder on YOUR computer, sure, no problem. At that point it's nothing more than content in a folder.

But Bridge cannot access the contents of a folder in the (DropBox) cloud.

But keep in mind that Bridge would have no idea what to do if you were working on a file in Dropbox on your computer and that shared folder was available to someone else and someone else were working on the same file at the same time on their computer. You MUST coordinate between anyone else as to whom is working on any given file at any time so that no one else is working on it as well.