Maybe powers are "bestowed" by spirits/gods/whatever you would call these otherworldly beings.  They are there from birth, or early childhood at least.  But most people never learn where their magic comes from.  Some people do, and seek to please the spirits in question, thus giving you covens who have staunch religious beliefs, but also covens and individuals who have no particular beliefs at all.  

The traditional idea(European/colonial American, anyway) is that witchcraft is done by making pacts with devils, so this would sort of resonate with the old lore, though with a sort of tweak.