Umm... It's possible to dodge a bullet in a round about way.
Step 1: Don't get into a fight with someone with a firearm.
Step 2: Repeat Step 1 ad infinitum.
Now, if you want the military answer:
At close range, you don't dodge a bullet, you keep your body away from the vector of the firearm. This is why someone with a firearm should never do the hollywood thing and place the muzzle directly on their target. This impedes their reaction time. Either way, you must either IMMEDIATELY seize the weapon, then shoot/stab them yourself. Regardless, your chances of getting fragged are still pretty high.
CIVILIAN APPLICATION: Utilize Step 1, as above.
At long range, you keep something between you and the firearm, OR, if you must move in the open, either low crawl or, if running, do so in a zig-zag pattern, preferrably with covering fire. Again, your chances of getting fragged are still pretty high.
CIVILIAN APPLICATION: Utilize Step 1, as above.
But, no, you will not play Super Cyborg Zombie Ninja and slice a bullet in half with your "Ninja-to"
Oh, and did I mention? Step 1: Don't get into a fight with someone with a firearm.