I shoot pistol, shotgun, and rifle with both eyes open. It's much more comfortable once you get the hang of it. I had to work on it in the beginning too, so here are two things I would suggest you try:
1) shooting glasses with scotch tape over the left lens will help get you comfortable with both eyes open but only let your right eye focus. You can gradually reduce the amount of tape on the left lens. The glasses I wear for trap just have a tiny piece of tape positioned just so it covers my left eyes view of the bead.
2) wear a ball cap with the brim pulled down real low so you're looking right under the brim. This one really helped me in the beginning. You're essentially helping your eye focus by reducing the aperture of your view.
Once you get your brain trained to focus on the correct target (ignore the double vision) you can ween yourself off the aids mentioned above. Hope that helps.