
Myth: "A gunshot can immediately kill a target"
People die from blood loss which takes many minutes. There have been cases where people are still able to move and react despite being shot multiple times. The idea of a gunshot immobilizing a rushing person only works in the movies.
http://www.ajc.com/news/news/national/man-continues-drive-car-despite-being-shot-twice/nnsbt/
Myth: "Guns are deadlier than Swords"
Because a hand-gun relies on poison through gunpowder and blood loss, it's less deadly than a sword. A sword can cut through flesh, cut arteries, sever limbs, damage internal organs, and so forth.
Myth: "Swordsmen must land a powerful killing blow to stop a target"
As I've learned in Sword-fighting, the goal is not to kill but survive. Usually, slashing an opponent will not kill. It's alot easier and safer to simply incapacitate an enemy than land a fatal blow.
With this in mind, imagine a gunman face-to-face to a knifeman. Who do you think will react quicker? It depends on so many factors such as who is more adapt to the environment, training, reaction time, distance, speed, the types of weapons, etc. One would expect the gunman to react faster as opposed to the knifeholder. According to the 21 foot rule, this isn't the case for officers. Officers must stand within 21 feet in order to stay safe from a knife-attack. Stand 15 feet near your attacker and you won't have time to pull out your gun. Officers have very little time to react and despite standing 21 feet, it is still dangerous.
Now imagine a swordsman charging in. The sword covers more distance and take into account what i said earlier. It only takes a few feet for a swordsman to quickly strike their opponent. Depending on how mobile your sword is, i'd say it's possible to strike a gunman from a distance.
How would the Swordsman get a slight chance of approaching the gunman without being stopped?
There's no way to "dodge" bullets. There's a huge chance your going to get shot and probably die from a gunshot wound. However your survival depends on many things such as speed, distance, agility, mobility, where you attack, balance, reflexes. Once the trigger is pulled, there is little hope of dodging bullets. Nevertheless, it's possible for someone to improve reaction time to guns. Who knows how this would turn out in a real life application, but it could minimize the number of gunshot wounds.
Guns move faster than humans, but a gunman does not. Thus there are many ways that can hinder him or her from firing an accurate shot. Moving too quickly decreases accuracy. Getting knocked off balance, distractions, or getting sand in your eyes can cause a gunman to miss shots. Shooting a moving target is even more difficult as opposed to someone standing still.
A study was done to determine whether or not running in a zig-zag pattern was more effective than rushing in a straight line. While running in a zig-zag pattern didn't make a much of a difference, it was slightly more effective than running a straight line. It surely made it less likely for a shooter to hit vital areas. This makes all the difference in landing a strike on a gunman.
There are certain shooting patterns that people have and are essential in moving out of the way before the trigger is pulled. If your a gunman, you surely don't want to miss your first shot if your not using an automatic. If your a swordsman, you don't want to dance around avoiding bullets. You also don't want to miss your first strike either.

I'm just speculating. Who knows if this will work in a real life situation. Regardless, i hope perhaps one day i can test this theory. Nonetheless, swords should not be underestimated in our modern age. Despite the advances of modern technology, a sword can be a devastating weapon.
http://readingwithavengeance.tumblr.com/post/87716139612/does-a-person-die-immediately-when-theyre-shot
http://prepcabin.com/2013/11/13/running-zig-zag-pattern-actually-effective/
http://writeworld.org/post/39568468890/a-summary-of-how-people-die-and-dont-in