I was able to get Continuity Camera working after troubleshooting Wi-Fi connectivity.
Initially, I had the issue where my iPhone 6+ (iOS 12) was not seen by my MacBook Pro (Retina, 13-inch, Mid 2014 on macOS Mojave v10.14.1) for Continuity Camera.
First, I logged out of iCloud on both, rebooted both devices, logged back in. That did not "fix" right away, but may have helped in the long run...doubt it though.
While BT was enabled on both, ultimately it seems to have come down to reboots and being on the same Wi-Fi (for some reason, my iPhone wasn't joined to the correct band/SSID in my home (I have 3 networks), even though it displayed the same SSIDs.
The fix: I had to forget Wi-Fi and reapply and then it worked just fine.
Overall, I feel like forcing log off of iCloud account was a healthy exercise, rebooting helped, and ultimately, forgetting and resetting my Wi-Fi connections helped to resolve my issue.
YMMV.