Looks like the three ways Macs become discoverable (showing up in other computers) via Bluetooth are Bluetooth Sharing, Handoff, and when the Bluetooth Preference pane is open.
To keep your Mac from being discoverable via Bluetooth, do the following:
- Select Apple menu->System Preferences...
- Select Sharing.
- Turn off Bluetooth Sharing, if it's on.
- Select View menu->General.
- Turn off Allow Handoff between this Mac and your iCloud devices, if it's on. (This option won't appear on older Macs.)
- Keep Bluetooth Preferences closed except when pairing with another device.
You can check discoverability from another Mac as follows:
- Select Apple menu->System Preferences...
- Select Bluetooth.
- Wait a while to see if your computer appears.