I'm too worried about a mishap to my camera or lens to carry it on a strap while riding my bikes. I do carry the camera and lenses in a rack trunk I modified with foam padding for protection. I had the camera and lenses in the trunk when I crashed at about 16 mph, and though my handlebars were twisted around and I bashed up my arm and shoulder, the gear was completely unscathed. Being behind the saddle seemed the least risky place to me.
Here's how I outfitted the rack trunk to carry the gear.
If I WAS going to carry the camera on its strap while riding, I'd be glad to have used climbers' webbing for the purpose --
here's what I did -- figuring that if it will hold my weight in a climbing fall, it'll do for my camera, too. It's soft and strong, and doesn't cut into my neck, either.