The main thing about competing is experience. In order to get to a level where you can compete and win, you have to get some experience by going to competitions. Try to pick some competitions that are local and not so upscale. If you can go and win, winning will build your confidence. Try to do it locally and then you'll be able to go from there.
For a lot of people, the junior rodeos, high school rodeos, college rodeos, amateur rodeos to pro rodeos are just steps that they take, if you're starting at an older age, just start out small. Something close to home where you can compete in a relaxed environment.
As far as the mental aspect of being nervous, if you're nervous, it's a sign that you're scared to do something. I would say you should think of yourself as being anxious to compete rather than nervous. If you're anxious, that means you are wanting to compete. What you can't do is let that anxious feeling become anxiety. You have to learn to control your feelings and anticipate roping instead of being too anxious for it. If you think about it too much, you overrun it in your mind. All it boils down to is roping and keeping your head clear so you can perform.