I have two eyes, and they both work, but they don't aim in the same direction. I have normal vision maybe a third of the time; other times it's double (one image above the other) and I have to close one eye to eliminate one image and figure out what's going on. I've been riding that way for two years or so. Some observations:
Peripheral vision was worrisome at first, and I'd still rather have it, but you can compensate with a mirror and by taking a lot of pains to look all around you before you make a move. I'm still working on it--I used to sort of enjoy city traffic, but I avoid it now.
Depth perception, or the lack of it, doesn't bother me much. You may get used to that fairly quickly. But since I can often get a fleeting instant of binocular vision, maybe not. Even a fraction of a second helps me get oriented.
I stayed off the bike for about six months in hopes things would get better. When they didn't, I started riding around the neighborhood on uncrowded roads to get the feel back. It took awhile, and I'm still not as comfortable as i once was (I've been riding since the early '70s, so I'm pretty much at ease on the bike). I may never get back to the kind of exploration and mountain bike riding I used to do. But if I pick my spots and times, I can still ride. And a guy I know, who lost one eye as a kid in elementary school, is a really strong rider who does at least 4000 miles a year in our short season, so it CAN be done.