Hi Allen, I'm a fellow Bear user and thought I would try to help out. I've noticed syncing lags before, especially with notes that contain a lot of attachments and/or large attachments. So if you have tons of notes with attachments, this could explain the syncing delay. Inside the note, you should see the placeholder for the image or attachment. Do you? A slow internet connection would also slow syncing down. Try leaving Bear on the screen of your iOS device and in an open window on your mac. I'd also not let my mac go into sleep mode, and would set my iOS device's screen Auto-Lock to never, but that’s just me and may be unnecessary.
I had the same problem as Allen (macOS Bear wouldn't sync, last sync was over 4 days ago) and it turns out it was my VPN on my Mac -- thanks for the tip Bob! Disabling the VPN (Private Internet Access) fixed the problem.
Anyone know why using a VPN would cause problems with iCloud sync?