Well, the bow is less about your dominant hand and more about your dominant eye, which isn't always on the same side. Basically, your eyes working together "center" your vision between them, but they will base that centering more on one eye than the other. If you point at a distant object with both eyes open, and then close one eye without moving your finger, your finger should appear to move away from the object. If it doesn't, then the eye that's still open is your dominant eye, and is the side you should be using to aim.
My husband is the only person I've ever met who can aim equally well with either eye.
with my recurve i shoot instinctively
whereas with my compound bows i shoot through a peep sight
and regular iron sight with the cross bow
You have to shoot non-compound bows instinctively. If you try to hold the arrow drawn and aim, you'll throw it off entirely. Primitive-style bows require you to shoot them thousands of times - or more - until the bow and arrow become like extensions of your body, and you just "know" the best way to get the arrow to the target.
I shoot archery with the SCA, so no technological advancements are allowed. The bow has to be a style that was used in the Middle Ages, made of wood and other natural resources (although they make allowances for the fact that very few people can afford an "authentic" bow and have to use laminated pressed-wood from modern manufacturers), with wooden arrows (they will allow fake-feather fletching, since real-feather can be tough and expensive to get). Let me tell you, quality wooden arrows are a BITCH to get hold of. Except for a handful of companies who service the recreationist community, the majority of wooden arrows are intended for things like Boy Scout and YMCA summer camps, and they're cheap garbage.
You have to shoot non-compound bows instinctively.
way back when you could get sights for them
i never used one though i always shot instinctively
If you try to hold the arrow drawn and aim
i found if you hold the bow too tight you will throw off the flight of the arrow
i hold any of my bows with just my pointing finger and thumb
when shooting instinctively you still aim but through an imagined path of flight
accuracy involves a repeated and established anchor point and a
consistent form and intense focus on your target
You can still get sights for them, although like I said, the group I shoot with doesn't allow their use. And even with a sight, it's still not advised to hold the draw more than a second or so.
I don't really hold my bow at all. I have a strap attached to it that loops over my wrist. I snug it into the web between my thumb and index finger, with my fingers lying on either side and pressing just enough to steady the bow, but not gripping. When I draw, it pulls the bow back against the cradle I form, and when I release, the strap (which is pretty snug against my wrist at all times) catches the weight of the bow on my wrist and keeps it in my hand. It prevents a grip that would create a "jerk" on the release.
I shot a bullseye the first time I ever fired a bow. The only reason I don't rank higher in my organization is that I really, REALLY need to build my back muscles enough to let me draw a heavier bow. Mine is 28 pounds, and simply doesn't have the heft to provide accuracy at the farthest distances. I have a sweet 45-lb that was a gift, but I can barely move the string. I can fire a 35-lb, but only for short periods of time. I need a new bow, and I'm really considering just upgrading to the 35 and working it as much as I can stand, to work the muscles.