The 192.168.100.1 address is for management access only and has no relationship to the Internet traffic. It was probably picked because .100 isn't generally used on small networks.

I had a Cayman router configured as a bridge and it worked exactly that way. 192.168.200.222 was it's address so I could access it, check status and reprogram if required. This was completely independent of the Internet traffic which used a 192.168.200.98 gateway, a Linksys router that got its WAN side address and gateway from the ISP through the Cayman bridge.

The Cayman cared not at all about the IP addresses, it just figured out what was on each side by MAC address, than found the IP address associated with those MAC address and bridged between the ISP and the Linksys. Any traffic inbound not addressed to the Linksys and any traffic outbound not addressed to the ISP gateway it just did not pass.