Masters in bows fire "you won't escape" arrows rather than "double damage" arrows. The arrows in the double arrow are a bit divergent, they do not aim the same target. That's why you usually hit only with one arrow, nevertheless, you hit more often.You can hit the same target with both arrows. IIRC, if you do then the caused damage is evaluated as if you had fired two arrows subsequently. Therefore, the damage caused by the second arrow can be different from the damage caused by the first one.
Mastery in Bows is especially productive if you fight a pack of enemies. AAAC can put an end on such pack before the pack succeeds to get to a melee distance.