Double taps are something that can really only be trained in live fire. One of the best pieces of advice I can give you break down into 3 things.
1. Learn where your trigger reset is and what it feels like. No sense in completely releasing the trigger with 1/4" will do.
2. Learn what it means to "follow through" a shot. Follow your front sight and time your second shot. Don't let the weapon snap and don't actively fight the recoil, just let the gun do what it does and tell it when it's okay to fire the second time. Hickok45 did a great video on "follow through" on Youtube.
3. Don't be in a rush. Lot's of people think that "double taps" are just 2 really quick shots, when in reality a true double tap is two "well-aimed" shots in quick succession. Start off slow. Work the fundamentals. Learn that trigger reset, work on following your front sight, work on your timing and handling the recoil. Speed is a byproduct of enough practice. Once you've got these things down you'll find yourself speeding up, but don't be in a hurry to gain proficiency. It will come. It's not easy to do well, but with enough training, it is a very effective technique.
I hope this helps you. Also, on the range I go to, we aren't allowed to draw and fire either as no weapons are allowed in holsters (they've had some incidents). No REALLY big deal to me, I practice drawing at home. What I do do at the range is practice from "low ready" which is where you draw your weapon to you (~30 degree angle holding with single hand just above your strong side hip). Bring the weapon up to aim and squeeze off a shot (or double tap). Then bring it back down to low ready. Even though you can't draw and fire, this will help you with the skills involved without actually gripping the weapon from a holster.
~LT
