I'm not certain why Garmin says the Bluetooth is another source that one should turn off if you want to get the most out of your battery capacity. Bluetooth in itself is a very low power user even for transmissions. However if you use Garmin's live tracking, that might be making many BT transmissions all during the ride to the Garmin phone app if it's handled by the Edge.
So if you turn off BT, you won't have live tracking provided by your Garmin Edge 530. I don't know whether the Garmin App on the phone has the ability to use the phone GPS to do live tracking.