Interestingly, it looks like it's the Bose unit that's stuck (possibly after being turned into a zombie by iOS 8.4 via bluetooth).
Annoyed by the bluetooth glitch, I plugged an audio jack in the AUX port on the Bose unit, but no audio came out. It looked like the Bose unit wasn't capable of producing audio anymore.
I reset the unit by long-pressing the MUTE button (hold it a couple of seconds.. it's more seconds than you expect, so don't give up). When all the leds start flashing rapidly, you can let go.
After this reset procedure, my unit restarted with a zero volume setting; I just needed to press the [+] button to raise the volume and now everything is working again, even via bluetooth.
I never liked Bluetooth as a technology because while it's supposedly handy, it's terribly flaky, either by design or because of poor manufacturer implementations — I don't know. Somehow, Apple and Bose really don't match very well over bluetooth. My experience with the Bose Soundlink and my rmbp is maddening.
And Bose's firmware update software is malfunctioning crapware.