Can bicycle riding 35 miles a few times a week be bad for my back?

Possibly. The answer depends on your posture and form as you ride, as well as how well the bike you're riding fits your body. Back pain often arises from poor posture or forcing the muscles that are mainly used for posture to bear much heavier loads. If you are hunching over the bars and feel a strain in your low back as you ride, you could easily develop pain or stiffness and you can easily injure yourself.