Sonos is expecting an SMB path.
If TM is on an Airport device (I assume that is what you are doing here), make sure Disk Sharing is enabled.
I am guessing the network host (Airport device or NAS) is named "the bughouse" (if it is an Airport device, this would be the Base Station Name) and the shared (ie root) folder is "bughouse backup" (this is the name of the drive you entered when you formatted it in Disk Utility)?
In Finder, you would see "the bughouse" in the Shared section of the sidebar, and when you click it, the "bughouse backup" folder would be at the top level of the drive? And, I would assume the IP Address for the Base Station is something like 192.168.1.1?
Sonos expects something like:
\\192.168.1.1\bughouse backup\sleep noise\...