The engineering and physics are obvious for helping you deal with the mechanics of the bicycle and aerodynamics. A major mistake engineers and physicists make in studying the function of the bicycle is that they forget to include the human being as a functioning part of the bicycle. This requires understanding the science of Kinesiology or biomechanics. These people have come up with some unreal ideas for modifying the bicycle over the last few decades. Chemistry and biology are very helpful in understanding the function of the human body at the molecular level.
Human anatomy is important for understanding the structure and mechanical function of the body.
These are also prerequisites for some of the following biology courses. Exercise Physiology Sounds foreboding, doesn't it. All you are doing is studying the function of the human body in relation to rest and exercise. Most people can learn it. If you can't find a good course in EP, a course in regular physiology beats nothing.