The main reason why all forms of fitness are not considered “Mind/Body" is because of the intention set in the workout, and the goals of the practitioner. Most mind-body fitness programs are not targeted at fitness as much as they are comfort, relaxation, and a sense of inner calm.
Cycling, on the other hand, is primarily about getting from point A to point B. While much of the beauty of cycling rests in its simplicity, there is something to be gained in focusing the mind more internally. The imagination comes alive when we move, and frequently emotions we are unwilling to face in daily life are able to come to the surface while exercising. There are many reasons why physical exercise is a great stress reliever.
You may want to consider setting an intention for your next ride. A positive present-tense mantra you can think of while you're moving, such as "I am free of tension" or "I am full of grace" can bring wonderful results to a mundane cycling commute. Allow yourself the freedom to explore where your workouts lead you mentally and emotionally as well as physically.
A key part of mind/body fitness is the coordination of movement with breath. In his Book “Yoga Anatomy,” Leslie Kaminoff of The Breathing Project defines the act of inhalation as the re-shaping of the torso and abdominal cavity to make room in the lungs for the intake of air. Likewise, inhalations generally coincide with movements that are opening, expanding and lengthening. Exhales are joined with movements that are collapsing, “crunching” or folding in.
Bicycling includes an expansive movement that is almost simultaneous with the contractive movement with the down stroke of one pedaling leg, and the upstroke of the other. This makes synchronization of movement and breath a bit difficult. Luckily, however, there is also a nice sense of rhythm in the upward and downward strokes.
One kind of yogic breathing is called Samavritti, or "same fluctuations". This is where you try to match the duration of the exhales with the duration of your inhales. You may want to practice this resting prior to your ride to help you center and set an intention for your ride.
The fifth and final component of many types of mind/body fitness programs is a basic belief in a form of life energy such as prana or chi.
In "Yoga for Cyclists (...and Cycling for Yogis)" Kathleen Ellis describes the three energetic tendencies of speeding up, inertia and a balance of these two forces called sattva - where you are able to move at your natural pace without hindrance. Vigorous exercise like cycling can lead to a revved up feeling, and an ungrounded state of hyperactivity.
To balance out this energy, yogis recommend that cyclists do something that they find relaxing, restorative, and grounding following their rides.