The biggest thing you can do to increase your speed is learn to spin, rather than mash on the pedal - read the thread about learning to spin and saving your knees. I know I was able to increase my speed by about 6 mph on avg when I learned to spin! And I can now spin my bike up to about 28 mph on a level road!

To be able to spin you have to have clipless. Toe clips or platform pedals without clips won't work. Basically, you pull UP on the backside of the pedal rotation to increase the power that gets transferred to the pedal. You manually move the pedal through it's entire rotation, rather than letting the leg take a break for the back half.

Try pedaling with just one foot clipped in and see what it feels like. You have to force the pedal all the way around the rotation, rather than stepping on it when it comes to the top and front.

I just got my bike in March, and it is only now that the muscles in the back of my legs are more sore than the ones in the front after riding! That means the spinning is getting better! I can tell because I am also getting faster!