Years ago I wanted to get a bow and the issue was I am left handed but right eye dominate. The store owner said I could never do that I would have to learn how to shoot right handed. Well that feels like a little girl trying to throw a fastball. Recently I have seen all these new sights and red dot scopes being used and wondered if technology had changed in that area enough that I could use something like that and still shoot left handed?
Coming from someone who made the switch himself (switched from RH to LH), I would certainly recommend trying to switch to RH, especially if you're just starting out. With that being said, if you're simply not comfortable (granted it takes some time) with the switch, you will be more than fine shooting LH, and simply closing your right eye. Plenty of guys/girls do it.
Ask him how I've managed to kill so many whitetails, squirrels, rabbits, antelope, elk, etc. with my bow over the years. Must be a miracle.
Honestly, you're better off learning to shoot right handed. It will only take a little while to get used to. Not fighting with eye dominance is just one less thing to deal with. Plus, there are far more bows and accessories for people who shoot right handed. Trust me.... I shoot left-handed.