I'm very concerned about rattlesnakes biting my dog while running! Am I being irrational?

If I understand your question, you and your dog like to do something which you believe to be dangerous(hence your question). I don't have a dog but I have children. I don't let them do things that are dangerous. My five year old really, really wants to cross the street by herself. She's all "grown up". And I'd love not to have to watch out for her. But I have to because it is my responsibility because I'm the one who knows better. And though I'm sure your dog is much more obedient than she is, she has to be obedient because if she isn't I will carry her under my arm if need be. It is great your dog is obedient, he must trust you a lot. So under these circumstances what is the risk? The risk is a snake will come out of the bushes and bite him. Your dog doesn't know the risk but you do. So what are you willing to risk is the question.