I am left handed but shoot a bow right handed. My reason for shooting right handed had nothing to with eye dominance but rather the availability of left handed equipment when I was a kid starting out. Couldn't find a left handed bow so I learned to shoot right handed.

I shoot guns left handed soI guess I am both eye dominate, if that is possible. I have shot a bow right handed for so long I doubt I could re-learn to shoot left handed.