I have my echo turn on like this all the time. There seems to be a bug with the echo with listening with it connected to a Bluetooth speaker. Once you stop the echo its fine BUT after around 10 minuets it starts playing again, on its own. It seems to be that when it disconnects form Bluetooth after being idle it starts playing again through its internal speaker. However this could re-trigger it connecting to the Bluetooth speaker.
Its a know issue and I'm surprised its never been fixed.
Biting the hand that feeds IT
