Do you have a place where you can practice draw and shoot, move and shoot, do timed reloads and shoot, etc?
Sometimes the facility where you hold matches is available for such practice.
Practice with dry fire (use snap caps if your manufacturer recommends) and start increasing speed gradually, while working on smoothness.
Find the pace where your form starts to have hiccups. Back it up one notch. Dry fire round to verify the back one notch pace is controlled and smooth. Try same pace live fire.
Repeat as necessary.
I know compglock17 and I already told you about the glass of water trick. Keep your knees slightly bent and your CG low when you move. Watch traditional martial artists or, for that matter, dressage horse riders and see how stable they keep their centers. Try to achieve that type of movement.
And have fun.