Bonus Attack Speed

is a Weapon Stat that affects the speed of the player's attack rate by reducing the | damage immunity frames of the entity hit.

It can be increased by holding items and wearing Armor with certain Reforges.

The maximum hits per second with and  can be calculated using this calculator:

Mechanics
decreases the number of invulnerability ticks an enemy is granted upon hitting them.

The formula for the invulnerability ticks of an enemy on hit is:

$${\forall BAS \in [-99,100], hurtResistantTime = \lfloor \frac{10}{1+\frac{BAS}{100}} \rceil}$$

where
 * BAS: Player's Bonus Attack Speed
 * hurtResistantTime: Amount of invulnerability ticks

The max is 100%, doubling the attack rate.

Shortbows
increases the maximum rate of fire of shortbows (Artisanal Shortbow, Juju Shortbow and Terminator). With optimal left-clicking the base fire rate is 2.22 shots per second with 0 and it is increased up to 5.00 at 100. Similarly to melee hits, this increase in fire rate with is also incremental, not continuous.

When only right-click is held, the fire rate starts at 1.67 shots per second (12 ticks per shot) with 0 and is increased to 2.50 shots per second (8 ticks per shot) above about 50. It is believed that this happens because items attempt to cast their right-click abilities every 4 ticks when right-click is held continuously.

Trivia

 * Attack speed works on arrows, decreasing the time before another arrow can hit the target. This only applies outside Dungeons, because arrows do not grant invincibility frames in Dungeons.
 * Attack speed does not affect.
 * It is possible to have negative attack speed, and it will lower attack rate.
 * The Livid Dagger and the Zombie Soldier Cutlass are the only items that give 100%.