There are a number of drills that you can do to build your cycling endurance. Professional triathlon coaches like Joe Friel use many of these drills. These should be in addition to your rides, which should increase in speed and distance as you become more fit. Do this first drill on an indoor trainer. Unclip one of your feet from the bike pedal and place it on the floor. Put the bike in a low gear and pedal with your other foot. At the top of the pedal stroke, there is a dead spot that is difficult to pedal through. Focus on this spot as you pedal. When your leg gets tired--which probably won't take long at first--change legs. If you do this exercise regularly, you will see your endurance improve.