How to fix iPhone 6 battery issues after iOS 8.4 because of Apple Music

My iPhone 6 is less than 5 months old. I recently updated to iOS 8.4. After that, I see that my battery is dying much faster. When I checked battery usage, 'Music' app is taking between 45 and 50% of the battery. I hardly using the music on my iPhone, so this is a shocker. Before it was saying that the Music was running the background. I turned off Apple music to see if that made a difference, but that didn't help either, in fact, it got worse (From 40% to over 50%).

Please help me fix this.