Yea, B is still acting like a router if it’s creating those messages.
I wonder if it’s bridging mode is actually bridging, or if it’s doing something weird.
OP - how is router B cabled? If it’s a typical consumer device it has one uplink port, which you wouldn’t use (usually) for a bridge setup. Because really a bridge today is just a switch (they were first called switching bridges, and we got lazy and just say switch). Use of an uplink port implies routing, not sure if the router changes its config for bridge mode. I just don’t use that port when I need switching.