You do have to work hard to get faster but you don't have to do it all at once.
Start slowly...Once well warmed up increase your effort until you are nearly at the panting state and hold that effort for thirty seconds...recover for five full minutes of easy riding...repeat several more times then after full recovery continue your normal ride.
Try this two days a week with a day or two in between as recovery/steady pace rides.

You should notice your average speed and your strength improving after a several weeks.
It takes time to improve as well as intent to become faster...if that is what you want.

I'm 57 and still do intervals for fun...I don't use any sort of regiment any more but use a "fartleking" system http://running.about.com/od/speedwor...lekworkout.htm while it is generally for runners I've used it over several decades of racing/training as a less regimented and more fun way to do intervals.

Good luck and keep us informed.