If you use Siri, you can simply ask it to turn Bluetooth on and off. Just press and hold Command + Space keys to invoke Siri. Now speak Turn Off Bluetooth or Turn Bluetooth Off. Wait for desired time, invoke Siri again and speak Turn On Bluetooth or Turn Bluetooth On to enable it again.
There's a second, but a bit clumsy approach you can take, if you don't use Siri, or do not have an active Internet connection. (Using Siri requires an active Internet connection).
Enable Full keyboard Access to use Tab key to move focus to on screen controls. Go to System Preferences → Keyboard → Shortcuts and select All Controls for Full keyboard Access:
Now, you can easily toggle Bluetooth using keyboard by following these steps:
Press Command + Space to open Spotlight.
System Preferences. Select System Preferences.app and press Enter to launch it.
- Press Command + f (if required) to move focus to Search field. Enter Bluetooth and select the entry to open Bluetooth preference pane.
- Press Tab key to move focus to Turn Bluetooth Off button. Press Space or Enter key to turn Bluetooth off. Wait for some time, then press it again to turn Bluetooth back on.
Using this approach, you can toggle Bluetooth without touching mouse.