I have a Microsoft Sculpt Comfort bluetooth mouse used on a dual boot system (Ubuntu 16.04 and Windows 7).
When I connect and pair the mouse on one of the OSs, everything is fine and the mouse is auto-reconnected the next time I boot.
However, if I reboot on the other system and connect/pair the mouse on it, when I switch back to the first OS, the mouse is not recognized anymore and I have to delete it from the devices list then re-pair it to get it to connect. It's the same from Windows to Linux, or from Linux to Windows.
It's not a big deal since it works, but having to delete/reconnect the bluetooth device each time I reboot is quite unpleasant. Have you any idea to avoid this?