I knew an old fellow who since passed away. He was a right handed shooter but develoved cataracts in his right eye. What he did was get a 1" piece of aluminum bar stock and mounted it on the scope rings, got another set of rings and mounted the scope so it was offset. He could still shoot right handed but used his left eye. It was a pretty neat set-up.
I've also had a friend that was left handed and always shot a right handed bolt action. He could cycle the action pretty quickly but I've never known him to use more than one shot.
Being lefty myself, I prefer the left hand actions. The selection now is better than it was 40 years ago. Remington, Browning, Savage, Ruger, Sako, Weatherby and a few others now make left handed bolts.