Apple Music listening history

Its available to me off the menu in the header. click the menu icon, then click the clock icon in the pop-up. Previously Played Popup


Is there a bar on the bottom of the screen showing which song is currently playing?

iOS 8.4 mini player

If so you can try dragging that up and it should bring you to a screen that has more stuff on it.

iOS 8.4 full player

Click on the button that looks like three dots with horizontal lines to the right of them (it's to the right of the skip/fast forward button);

Up Next button

that will show "Up Next" if you scroll up you will see your History.

Up Next scrolling up shows History