Simulation with a paintball gun will really give you a feel for what you are up against when it comes to empty hand defense against firearms. I practiced this drill with a martial arts group a few years back.
Here is what we discovered.
If the gun is not drawn, attack. Do not allow them to draw the weapon. At five feet, with a paintball gun, it is almost impossible to get the gun out, up and aimed. At ten feet, this is still very difficult without training. At 15 feet, if the attackers reflexes are average, the shooter could fire on a quick attacker.
If the gun is drawn and aimed your options are limited by distance. At five feet, one can attempt to get off line and get control of the weapon. Against a live attacker with a paintball gun, I was hit five times for ever one time I got the weapon. At 10 feet, I tried twenty five times and got the weapon once. On the other hand, I ran in a curved path and was not hit 50% of the time. At 15 feet it was impossible for me to get the gun. However, I was able to evade 50% of the time.
Running is a good defense against the gun IMO if there is no other options and the weapon is already drawn. If you run in a curved path, the shooter is going to have to lead you in order to hit. The shooter will have a higher percentage of missed shots depending on the shooter's skill.