I think your breathing technique when shooting a bow depends on how you shoot the bow. If you shoot it in a very deliberate way, where you hold for several seconds at full draw before releasing, and particularly if you use sights or some substitute for sights such as gap, then a similar breathing method to that used when shooting a rifle would be appropriate. The idea would be to minimize movement while aiming.
If you shoot instinctively, perhaps using the swing draw method, and release as soon as you come to full draw and anchor, then I think your focus should be so much on the target that you have no memory of breathing, anymore than a baseball shortstop would as he scoops up a grounder and fires it off to first base.