Same issue here - Windows 7 32-bit Guest, Parallels 15.1.1, macOS Catalina Host. Setting to 'Shared' network helps - at least it gets an IP (10.A.B.0/24). But this doesn't put the VM on the same subnet as the rest of the network (X.Y.Z.0/24). What I found to work was to the VM Configuration, remove the Network Adapter, and then add it back in.
Ugh Seriously... Same issue latest Dekstop 16 version. Windows 10 VM. It was literally just working, had a remote desktop session going to the VM. And had to reboot and when it came back it wasn't working. checked and "Bridged mode" is now grayed out...
Hello MichelleF1, Please be informed the heading Bridge network will be grayed out, you will see the Default adapter, Wifi and so on which you can choose under Bridge network. Please refer to this KB article: for more information: https://kb.parallels.com/8978 Thanks, Parallels Team.