Got this tip from some posts in Ubuntuforums.
Linux bluez stack has no way to turn off Bluetooth device via GUI. Normally we (at least, me) use Bluetooth for file transfer few times a day for very short period. Keeping Bluetooth enable wastes the extremely-precious laptop battery.
The solution is to create this shell script on your desktop. You can choose any name, meaningful or not. My script is called "bttoggle".