290s & 290Xs only, don't need bridges (280Xs still do, or so I've heard, haven't used any myself)
The cards actually physically do not have plugs for Crossfire Bridges on them, at all, so yeah...
It sounds to me like you didn't reinstall drivers with a cleaning after installing the second card? Or did you install drivers for the first time with both cards installed? Either way that's a mistake.
You need to test each card individually to verify they both work without issues, then once you've tested both thoroughly to make sure neither artifacts or has any issues, you uninstall drivers, use a program to clean leftover files like DDU, then reboot, reinstall both cards together in the system (after turning it off, duh), and reinstall the drivers. Then when windows boots up after rebooting for the driver install, a window should pop up TELLING YOU Crossfire has been enabled.
If that doesn't happen, something isn't working right, because it has always happened with 2 or more cards installed in my system.
CPU: i7 3930k @ 4.6GHz 1.29V (Corsair H110-cooled) ~ Motherboard: Asus RoG Rampage IV Extreme
RAM: G.Skill Sniper Gaming Series (4x4GB 2133MHz, CL9) ~ PSU: Corsair AX 1200W ~ Case: Enermax Fulmo GT
GPUs: 3x HIS R9 290X Reference (Core) Editions in TriFire, Max Load Temps: 71C/70C/71C during OC testing :-P