I have two answers in mind for this question:
Muscular Energy into Kinetic Energy
Muscular Energy into Mechanical Energy
Which answer will be more appropriate for this question?
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One more point that has not been made yet is that you need to be clear about what system you are considering: Are you looking at a system that just includes the person, with interfaces between the cyclist and the bike at the cyclist's hands, feet, and buttocks, and the rest of the cyclist's surface with the surrounding air? In this case the majority of the work done by the cyclist's muscles ends up as mechanical work done on the bicycle's drivetrain.
Or, are you looking at the bike, which has the above interfaces with the cyclist, plus the contact points of the wheels with the road?
Notice that at higher speeds (say, 20+mph) the vast majority of the work done by the cyclist is against aerodynamic drag, plus some work done against drivetrain friction and rolling friction, all of which ends up in thermal energy. As a matter of fact, when riding on a level road at constant speed, eventually all of the cyclist's work ends up being dissipated.
In any case, kinetic energy of the bike-rider system is only generated when the bicycle is accelerating. When riding at constant speed, only kinetic energy of the air disturbed by the bicycle/cyclist's motion is generated. This kinetic energy is then dissipated in fairly short order.
Mechanical energy usually means the sum of the kinetic energy and potential energy.
So when you ride your bike you hope that the muscular (chemical) energy is converted mainly into mechanical energy. Unfortunately friction will produce heat and sound and will reduce the amount of mechanical energy that you have.