Constant Bluetooth Connection Request Prompts Between Two Macs

Solution 1:

I had a chat with Apple Support. They suggested deleting this file and rebooting the affected machines:

/Library/Preferences/com.apple.Bluetooth.plist

This seems to have worked. Deleting the file does not cause any problems - it gets regenerated on startup, and all my Bluetooth devices still connect fine.

Solution 2:

Continuity and iCloud are the obvious paring agents, so I would disable handoff first on both devices and see if that quells things.

If so, you might need to engage Apple Support to see if there’s a precise way to rejigger that, but for most people you would need to sign out of iCloud on one or both Macs to then sign in again and see if the pairing identity crypto can heal itself.

Solution 3:

If you hold the option and click the Bluetooth icon in the menubar, you can see whether your computer is discoverable by other Bluetooth devices.

Since Mavericks, Bluetooth discoverability is determined by whether you have the Bluetooth preference panel open. Other things like continuity and Bluetooth sharing might also have an effect on discoverability.

In my case, removing the Bluetooth preferences .plist file and rebooting seemed to work, but only because I didn't have the Bluetooth preference panel open after I rebooted.

Just FYI, holding shift+option and clicking the Bluetooth menubar reveals a "Debug" menu that allows you to reset some aspects of the Bluetooth system.