This is a splash screen that gives you an option to join Apple Music or skip and go to your music. Since the options aren't showing up for you, you'll need to force quit the Music app, reboot the phone and then go to Settings > Music > Show Apple Music > Toggle it OFF.
Directions for force quitting an app:
1. Press the Home button twice quickly. You'll see tabs of your recently used apps.
2. Swipe from left to right until you find the Music app.
3. Swipe up on the app's preview to close it.