Bluetooth audio is not supported on OpenELEC. What? in such a modern OS!? ..my laptop/desktop/phone/tablet/etc. has supported this for years!!!
Yup we agree it is a little stupid, but (and it's a big but) supporting Bluetooth audio under Linux requires pulse audio (not alsa) and to use pulse you must compile Kodi to exclusively use pulse audio. If you do this Bluetooth audio works (yay!) but pulse only supports 2-channel stereo output so you lose all the multi-channel (5.1, 7.1, etc.) output capabilities in Kodi (boo). As multi-channel support is rather fundamental to a mediacentre distro like OpenELEC and the project team does not have the manpower to release both normal and pulse builds; we only release builds compiled to use alsa that include multi-channel audio support.
Should things ever change to make Bluetooth audio a sensible addition we will add support, but for the foreseeable future this is not going to happen.