Parallels was unable to provide help on this, but I needed a workaround and here it is. I have only been able to reproduce this bug with bridged networking.
Parallels is reading the "Default" and "Ethernet" adapters incorrectly. I am close to figuring out the pattern, but even creating an "Ethernet 2" does not help. The workaround is to use the wi-fi adapter if "Ethernet" is your primary or "Ethernet" if wi-fi is your primary.
Steps to fix:
Assume: Connection to the Mac is wired and "Ethernet" is the Mac's primary network.
Enable Wi-Fi and allow it to connect to your network. You will have 2 IP addresses, but as long as Wi-Fi is later than "Ethernet" in the "Set Service Order", you are all good.
For the network of the guest machine, choose "Wi-Fi". There is another tiny bug where you may have to select it twice if the machine is active. Make sure it was selected.
Bridged networking will now work, albeit over wi-fi. I intend to experiment with a second physical network adaptor, but for right now I just needed my virtual machines up and running.