There are several ways to do it.
Probably the best would be adding "damage" instance variable to bullet object. When the bullet is fired (spawned) set a value to this variable. For example, without the powerup your bullet.damage=10, with powerup bullet.damage=20
When the bullet hits an enemy, substract bullet.damage from enemy's health.
As for the powerup itself, this also can be an instance variable on your character object, or a global variable.