I am right eye dominant and right handed. My Dad is left handed. He wanted to try Trad Archery so, I bought him a couple of left handed bows. Before I shipped them to him, I tried it out. I got real close to the target, maybe 10 feet away. I shot no where near where I thought I was shooting. Then, I used three fingers under to bring the arrow up high on my cheek and I closed my right eye, bam! Bullseye!
The important part of the story is..... you can shoot either side, you just have to make adjustments to how you shoot. Find out what works for you.
I keep one lefty around for fun. Plus, I think it helps me draw a RH bow because I am strengthening both sides of my back muscles. Marlon Torres suggests this as a way to increase your draw power.
BTW, its kind of cool to be able to shoot both sides. I did that at a 3 D Shoot - on the range - and then everybody tried it.