Both RideWithGPS and Strava can be backgrounded, and still work. Both have live maps that you can see where you are (best with phone/net service).
RideWithGPS has a mode called "Handlebar Mode" which if you enable it, you can see the app by simply turning on the screen.
Strava needs the screen swipe (or RWGPS without the Handlebar mode also takes the swipe).