This is how to turned off Bluetooth by default in Ubuntu-Mate 16.04.
Open the terminal and run the following command
gksu pluma /etc/default/tlp
Then find the following section
# Radio devices to disable on startup: bluetooth, wifi, wwan.
# Separate multiple devices with spaces.
#DEVICES_TO_DISABLE_ON_STARTUP="bluetooth wifi wwan"
Edit the last line as follows (including removing the leading #):
DEVICES_TO_DISABLE_ON_STARTUP="bluetooth"
Then save and close the file.
You also need to stop the Blueman Applet from loading at startup as it will turn on bluetooth when it loads. This can be done by unchecking it in Startup Applications Preferences. It can be started anytime after that by running the blueman-applet
command.
Reboot for all this to take affect and you should be good to go.