I can get dressed in the basics and out the door in 30-60 seconds. When I get ready for bed my clothes and everything get left bedside on the floor (except for phone and EDC which go on nightstand) for something like this. If I get a phone call for an emergency - Once I get up I can get dressed and get out the door with EVERYTHING I usually carry In less than a minute. If I hear something out of place at some strange hour of the night and have to go check on it, All I grab is Pants boots gun light (Jacket if its winter) and I can be out the door in less than 30 seconds.
To practice getting up and out QUICK - When your alarm goes off when its time to wake up see how quick you can hit snooze (like grabbing the phone) get dressed as quick as possible and get out the door. See how fast you did this and if you have everything you need. It takes a little while to get used to doing it since you havent really woken up yet, but you WILL get used to it. I had the luxury of working EMS, so when the alert system went off it was out of bed boots on and out to the rig in about 40 seconds. Same thing if I was in the shower at the station. This just carried over to phone calls late at night or having to check on something strange.