Any good shooting coach will tell you this, learn to shoot the bow left handed. However, my neighbor who is in the same book as you, shoots with an eye patch over his left eye.

tkycaller asks a good question....you'll need to use your right eye with a right handed bow, either close you left eye or use an eye patch, or like mentioned, shoot left handed. I'm sure with time, you'll get it since your already shooting the rifle and handgun left handed.