Hi profbg,
Thank you for posting in the Apple Support Communities. As I understand it, you're finding you hear audio from the Music app at unexpected times.
Does this only happen when you're on a call, or does it happen at other times as well?
How frequently would say this occurs?
You mentioned a Bluetooth headset. Try tapping Settings > Bluetooth. I'm wondering if your device might be automatically re-connecting with a Bluetooth device and starting playback. Try forgetting the connection to any devices you see under Settings > Bluetooth to see if that helps as a way of narrowing things down: Pair a third-party Bluetooth accessory with your iPhone, iPad, or iPod touch
To unpair a Bluetooth accessory, tap Settings > Bluetooth, find the device you want to unpair, and tap the info button
, then Forget this Device. This will remove the accessory from the list of available Bluetooth devices.
To add the Bluetooth accessory to your device again, place it back in discovery mode and repeat the steps above to pair it."
Hopefully this helps! Kind regards.