Blocking the negative thoughts is only the first step. Sometimes people don't hear or are not told the most important part, which is replacing the negative with the positive. How you do this is very personal. Some people use a mantra, some just repeat a saying in their head that isn't so "mantra-like," and others use visual images. You have to decide. As Catrin said, when you are riding, it is easier to focus on the visual spectacle of the environment. We really do see things on a bike that we miss otherwise. Same for hiking, or even walking.
Research shows that you can decrease anxiety/repetitive negative thoughts by using what's called 4-6 breathing 10X a day for one minute. This means inhaling for 4 breaths and exhaling for 6 breaths, slowly. The key is to always have the exhale be longer than the inhale. You can actually see changes in the frontal area of the brain on an f-MRI (forgive me, I forget which specific part) after a person has been practicing this for 4-6 weeks. Of course, it takes a commitment to do this, but it really works to bring down your overall level of anxiety and hypervigilance.
And, from my personal experience, mixing up activities is always best. It keeps us from physically over using the same muscles and joints, but also gives our brain the variety it craves.