It is recommended that you use a wired USB headset as this will provide the best Jigsaw Experience (See: Jigsaw System Requirements). If you choose to use a Bluetooth headset, it can be more fickle during the session than a USB type. Things to consider with a USB head set is battery life, going out of range, or the Bluetooth connection can be "taken" by another device (like your mobile phone or tablet).
How to Enable a Bluetooth Headset for Mac
Make sure the device/headset is turned on.
Go to Apple Menu>System Preferences
Click on Bluetooth to turn Bluetooth on
Find your headphones and choose it, as the "Output Device" for your Mac.
In Jigsaw, your microphone selection should be set to "Default" (don't actually choose the AirPods or your headset's name, because they are already set as the default for the Mac).