How do I delete all Music off my iPhone library so nothing appears?
I had no choice but to remove all music from my iPhone. I have had music intrude in on my 3rd party apps playlists and even phone calls on bluetooth in multiple vehicles. This is a ridiculous solution to a problem I hope is fixed soon.

I tried to go straight to step 5 but Music app was not in the list for me delete to select (iPhone 6 plus iOS &lt;= 8.1.2)


Settings > Music - toggle "Show All Music" to off. 
Open music app - identify all songs that are on your device.
Settings > Music - toggle "Show All Music" to on.
Download the songs from step 2.
Settings > General > Usage > Manage Storage > Music > Edit > All Songs > Delete 
(Optional) Settings > Cellular - In "Use cellular data for" locate Music App and toggle off.
Settings > Music - toggle "Show All Music" to off.