I actually have been bitten by a snake. Now, this is where the type of snake you're describing is terribly important. My sister and I used to catch snakes by the rock face of the buffalo jump in the Cochrane Ranche in Cochrane, AB, Canada. These are harmless little grey garter snakes. They would get POd at you fooling around with them and these little teeth would come around and *GLOMPF*, big mouthful of people. Unfortunately for the little guys, they have no jaw muscles and the tiniest teeth so we get no broken skin or diseases or even snake spit, if I remember right, and we just keep on fiddling around with the snakes. The biggest one we caught was over six feet long but it couldn't break skin when it bit you either. I never complain about having to bike there...it's someplace PROXIMATE to rattlesnakes, bears, cougars, etc, but you never see them anywhere near the town or where I ride. I saw a badger once, if that counts for danger points.
Unfortunately, I live in southern California now and I have almost stepped on rattlesnakes...twice. Let's just say that El Moro Canyon is off my hiking/biking 'must see' places.