My Apple mouse was connected to an old MacBook Pro and was never removed. I recently had trouble connecting it to my new MacBook Pro. This worked for me:
1) turn off your Apple mouse
2) open system preferences [cmd+spc, "system preferences", enter].
3) navigate to "Bluetooth", make sure Bluetooth is on.
4) hold down 'click' action on Apple mouse then turn on the mouse. Make sure you hold down the 'click' while it turns on.
5) You should now be able to `pair` your Apple mouse to your Mac.