Quick Bow's blueprint only begins to spawn once the player has died two times on a save file - this is because the starting room which contains the blueprint only begins appearing starting with the third run; the first two runs have custom starting rooms which do not have the secret area that appears in the normal starting room. The secret room is located on the left side of the starting room, climb up the wall using the platforms and you will reach a secret tunnel that leads to the blueprint.
If an attack with this weapon is interrupted within the first 0.15 seconds of the attack animation, another attack with this weapon can only be attempted at least 0.1 seconds after the start of the previous attack.