Tighten your core muscles. When you're first starting to learn how to spin really fast it helps to ride a hill you're intimately familiar with.
That way you know the point when you're really past the comfort threshold. You want to be able to moderate your speed until you're at a good distance from the bottom of the hill where you can bleed off your speed/cadence. I like to ramp it up and right as I get close to exceeding my comfort zone I tighten my core, exhale smoothly and quickly and can usually accelerate just a little bit more.
Also, raising your bars may help. On my prior bike I had a lot more bar drop and could always spin faster on the tops than in the drops. I raised my bars 2 inches or so and now I can spin faster in the drops. Hip flexors do a big part of helping your leg move around quickly and have an ideal firing point that comes with a lot more upright posture than a lot of people expect.
Alternatively, go Keirin style. Tie one end of a rope around the headtube of your bike, tie the other end around the bumper of a car. Have a loved one drive the car with specific intervals at speeds consistent with your training cadences. You'll be spinning in no time!