Chemical energy does not come into the picture while riding a bicycle.
The energy stored in the bonds of a chemical substance is termed as its Chemical energy.
It is the energy that allows a substance to undergo a chemical reaction and transform it into other substance(s).
No chemical reaction or substance is there while riding a bicycle, hence no chemical energy.
Heat energy is produced while riding the bicycle due to the friction between the tires and the surface of the road.
Mechanical energy is a combination of kinetic and potential energy. The energy by virtue of motion is termed as Kinetic energy and the energy possessed by virtue of a stationary position is termed as potential energy. Since the bicycle is in motion hence, Kinetic energy is present and also the Mechanical energy. [in this case, kinetic energy is equal to the mechanical energy, since potential energy is zero].