The phrase "bullet time" was coined by the Matrix movies, to indicate the animation style when the action would be slowed down so you could see bullets slowly flying past the characters as they dodged them. In the OBD, to be a "bullet timer" means you are fast enough to react to/dodge bullets. If a characters is a bullet timer, this generally means that at least their reaction time is above the speed of sound. Obviously, this is very important in matches.

Bullet timing is not a simple thing, it often requires a good amount of analysis to quantify. For example: What kind of guns were the bullets fired from? If the specific model of the gun can be identified, the muzzle velocity usually can as well. Otherwise, a general rule is that more primitive guns = slower, while more futuristic/advanced guns = faster. Bullets from handguns tend to be slower than bullets from larger rifles.

Also, you need to make sure that the character in question is actually reacting to the bullets after they were fired, instead of just dodging the aim.

The same principles can be used to analyze instances of dodging other projectiles/ranged weapons, but bullets are used more often since they can be directly compared to known values in the real world. Lasers are another weapon that is usually used for this kind of analysis, but since there are so many "psuedo-lasers" in fiction that don't conform to their actual properties, simply something being called a "laser" isn't enough to say it's moving at lightspeed, so bullet timing is a bit easier to authenticate and quantify.