I have the same issue and spent a long time on the phone with Ring support where they could not fix it and indicated that someone from their tier 2/3 support would call me - no one has - VERY disapointing.
I have many of the Ring devices (Spot Cams, Security Alarm, Doorbell, etc.) which all work as expected. The only Ring product that does not work is the Ring Bridge.
My ISP is CenturyLink. I have the Technicolor C2100T. I called CenturyLink and they claim they do not have any external FWs that would block traffic. I have reset my router to fatory settings. I removed my FW. I put the Ring Bridge in the DMZ. I put the router in bridge mode and connected another router. All does not work.
As previous community members have reported, the Ring Bridge first connected to the router, but devices failed to register, when I reset the Ring Bridge it would no longer reconnect to the router. I have to believe it is a firmware issue - Rings response was to send me a new Ring Bridge which had the same issues. I also bought another from a local store and had the same issues.
The Ring Bridge does consistently work when I connect it to my iPhone Hotspot. It not only registers with Ring but allows all of my lighting devices to connect. Although this is a good datapoint it is NOT a solution as I do not want to use my hotspot for this.
I would think that Ring would want to help resolve this but I am getting little to no support from the. Therefore, I was hoping that someone else in the community has experienced this issue with the CenturyLink modem/router (or other manufacture) and have had luck in getting this to work. If so can you please share what you did to make it work?