Well I'm left eyed dominate and shoot a rifle left handed, so I got lucky there, however shooting a bow seemed much more easy for me to shoot right handed since I throw right handed, and my right arm is my strong arm.
The guy at the bow shop told me, you need to shoot a bow with your dominate eye, just learn to shoot a bow left handed, it won't take long. He was right, I took his advice and bought a left handed Bowtech, by about arrow 100, it now seems completely natural to me. I say go with your eye, your muscle coordination will come, but your right eye will never get stronger than it is now.
