I'm told I need to enable Bridge mode on the cable provider's modem. IS this true?
Yes, if you want the Time Capsule to function as your network router. However, some modem/router products cannot be configured to operate in Bridge Mode as a simple modem....and some providers will not support this type of setup.
So, you will need to get in touch with the support folks at your new provider and ask them whether 1) it is possible to configure the modem/router to operate only as a Bridge Mode modem.....and 2) whether they will help you and offer support for this type of setup.
An even simpler solution might be to swap the modem/router for a simple Bridge Mode modem, if your provider offers that option.
If it turns out that the modem/router cannot be configured as a simple Bridge Mode modem, or the provider does not offer a simple modem only option, then your only option will be to set up the Time Capsule in Bridge Mode. In this setting, the Time Capsule can still provide a wireless network and back up your Macs, but the modem/router will actually be charge of your Internet connection and network devices.
Do I need to set up something special on the Time Capsule?
Since you have changed providers and will be using a new modem, the Time Capsule needs to be reset back to factory default settings and then set up again, so that it will pick up the correct Internet settings from your new provider's modem.
You can probably use the same names and passwords on the Time Capsule that you used before, and the Time Capsule reset will not affect any of the data stored on the Time Capsule hard drive.