Humans are designed to walk forward with their heel, ball, and then their toes coming in contact with the ground and your center of gravity works this way. The problem with trying to walk in reverse is that your center of gravity will eventually overcome your feet and your body will fall back. Shooting on the move, going both forward and rearward requires your knees to be bent to act as a shock absorber. If you try to walk upright in a normal stride, there is too much bounce to stabilize the handgun properly and get any type of accurate fire.
Due to this requirement, when walking backward, your hips will be lower and will actually proceed the shoulders, chest, and head region to the rear. While this technique works great on a nice flat range when no stress is evident, in a time of life-threatening events, your body is going to move faster regardless of your desire.
When shooting on the move in a forward direction, normal footwork should be used, as it is always a good idea to do whatever you do normally. In the case of shooting on the move in a forward direction, you will merely bend at the knees and lower your center of gravity, which will stabilize the weapon outstretched in front of you, then walk across the ground in a heel, ball, toe configuration.
Remember that shooting on the move should be undertaken for a reason, normally to avoid incoming fire. So moving is probably 10 times as important as shooting accurately. Shooting will normally be done to keep your opponent engaged and to keep him or her from shooting back at you. But do not forsake rapid movement in the interest of trying to place a tight group on the bad guy.
Tactical gun skills are not magic. They just require some thought. You want to work this stuff out and plan your techniques on your own at the range under no stress. Trying to figure out some sort of tactical option when the bullets are flying over your head will tend to affect the efficiency of your thought processes.