Bridge Mode is the correct setting for your Time Capsule.
To aid in troubleshooting, I suggest that you temporarily move the Time Capsule close to the Uverse router and connect directly to one of the Ethernet ports on that device. Test to see if your wireless is working.
If yes, then move the Time Capsule again and this time temporarily connect to the Ethernet switch to test that way.
Keep working your way outward, testing as you go. If the wireless works on the first test when you connect directly to the Uverse router, at some point, you will find the connection problem. It's almost always something simple, like an Ethernet cable that is not making a good connection with one of the Ethernet ports.