Heel-toe walk, use your knees to absorb the bounce and keep you steady. Shoot when you have a clear sight picture - don't try to time. It will only slow you down.
If you have a shot timer, set two cones up five to eight yards apart. Put some USPSA or steel targets out there, 5-15 yards distance. Practice putting controlled pairs on each target while getting from one cone to the other. Use the par time function on your timer to help build your speed - if the par time goes off before you've reached the second cone, count that as a failed run. Hold yourself accountable for accuracy - put some sort of penalty in there for misses or rounds dropped out of the A zone. Keep running it over and over again, pushing yourself for the best score based off accuracy and making it to the cone within the par time. Keep dropping the par time until your accuracy becomes unacceptable. Give yourself a little more time towards the end and shrink the targets down in size (or push them back further) to end on an accuracy note.
That will get you moving steadily and shooting faster on the move.