As a non power of Mac (only recently switched), I'll definitely try this.

My repeated attempts to remove from Dock and hide it all failed: half the time I remove my ear buds the Apple Music pops up in the middle of my screen and auto-enables itself in the Dock...

The Dock just contains a bunch of shortcuts. The app itself lives in the /Applications folder along with the rest of them that you can choose to add to your dock (by just dragging them down there and letting a spot open up for it).