I, and a lot of other people are using the latest version of Photoshop CC and Bridge without any problems on El Capitan. You should start by resetting your preferences for both applications, which you do by holding command-option-shift as Bridge and Photoshop start. In Bridge, check all 3 boxes in the prompt that opens, and then click ok. In Photoshop, click yes in the "delete Photoshop settings file" dialog box and then click OK. This will reset each program back to its default configuration.
If that doesn't work, uninstall and reinstall Bridge and Photoshop, and also be sure you have installed all of the OS X updates by opening the App Store application. OS X should be at version 10.11.2, which is found under the "About this Mac" window in the Apple menu.
Do you receive any errors when you try to open Photoshop?