yes, i think you have the idea. Interval training. ride 20 seconds as fast as you can, followed by 40 seconds of recovery. That's one of the things we do in the spin class.
As you start really accumulating the miles, your speed will improve. Try doing 25 miles once a week every week, and some smaller rides in between. And then move up to bigger rides. And add hills. HILLS will make you stronger.