IDPA and IPSC are both very good venues to practice and be exposed to new challenges. HOWEVER it was my experience that very few would allow you to shoot “on the move” if anything you would get an elongated box that you might be able to get a couple rounds off from one end to the other. That being said the ranges that host these events are often “3/4 ranges” in that the range is “sided” on 3 sides which if properly constructed “can” give you roughly 220* of shooting flexibility. Unfortunately even if you have a properly constructed range LIABILITY for the range is a huge concern AND expense and often times it is written into the insurance policy that “thou shalt NOT shoot on the move”
Some may wrinkle their nose at this but here it is. Paintball, Laser Tag and Air Soft are ALL viable training options. Air Soft being the one that would be most realistic (short of “Simunition”). If you can find a CO2 powered “blow back” Air Soft pistol to match yours you could happily practice shoot n move just about anywhere.
For you urban dwellers a couple 5 gal buckets from Home Depot with a couple layers of news paper or similar is an effective “bullet trap”, I also recommend that you put a layer of packing foam (like gun case foam but from packages) in the bottom of the bucket. 5 gal buckets are also handy as he!! to hold water in the event of a hurricane / blizzard etc. and a whole lot more manageable than a 55 gal trash can full of water (1 gal of H2O = 8 lbs, 8 x 55 = 440 lbs vs 40 lbs for 5 Gal)