Bows are different to guns in the sense that they provide a constant energy, while the projectile provides the terminal ballistics.
Attaching AP to the bow is the same as attaching damage to the bow, that’s the expected AP from a mid-range arrow with the energy the bow can provide, and it will only be multiplied with different kinds of arrow/bolt, except in special cases.
Having it as a function of damage wouldn’t be terrible, but makes some things more difficult and is less obvious to the player. I.E I pick up a bow, and there’s no way for me to actually tell its AP directly, I have to do the math and might not know the equation, since AP isn’t the same equation as damage. Taking E.G 10% of damage and adding it as AP wouldn’t actually be correct.