That only works if the Bluetooth device is able to connect to two or more devices at the same time. My headset doesn't, so if I want to switch sources, I need to explicitly disconnect the headset from the phone and manually connect it from the PC (in both cases, open Bluetooth settings, click on theb headset that's paired and click either connect or disconnect). It's a bit of effort but not too bad. Not as bad as pairing though.
If I don't disconnect from the last connected device, my headset will automatically connect to it and only play media from it.