Welcome to Android Central! Are you using Google Play Music? That might be a little tricky, because I recall seeing some issues in the past from people who wanted to play downloaded music only, and found that the phone was still accessing the music in the cloud (and therefore using data). If you're using Google Play Music, you could first try switching the Downloaded Only option on (in the side menu). If it's still causing some data usage, you could instead turn on Airplane Mode (or turn off mobile data) temporarily while you're playing the music.