Energy use by muscles, actual work done by muscles and more
I speak only for the U.S. regulations: the calorie labels on wrappers refer to the energy released when burned. Sometimes these are inaccurate. Many dieticians recommend calculating the calories based on weights of protein, carbohydrates and fats in the serving: 4 kcal in each gram of protein and carbohydrate and 9 kcal in each gram of fat in your food. Multiply carbs, proteins and fats by the appropriate value and add them up.
The reading on the bike does not take into account your pulse. Just the raw work done turning the pedals. Some very smart bikes do take pulse into account, but the often inaccurate heart monitors lead to inaccurate calculations of total energy.
The heart and diaphragm (muscle primarily responsible for breathing) do use more energy when exercising than when you are sitting still. But that increase is small relative to the increase in the primary muscle sets involved in the exercise. Your resting heart rate is probably around 70 bpm, your exercising heart rate is probably around 160-180 bpm. So it has increased its rate and energy consumption by about 3 times. Your skeletal muscles maintain a basal metabolic rate during inactivity (one purpose of this is your body needs the heat from slightly tensed muscles to thermoregulate itself) - but during exertion, their metabolic rate increases enormously. Exercise increases their energetic demands by whole orders of magnitude.


The actual value of the (energy used by heart) / (energy used by skeletal muscles during exercise) depends on what exercise you do and how efficiently you do it. The change in the ratio between inactivity and activity depends on how much muscle mass you have (more muscle uses more energy during inactivity) and how strenuously you exercise. But the point is that the increased energetic demands by skeletal muscles far outpace the 3x increase in energetic demands by the heart and diaphragm - so the latter accounts for pretty much all total energy consumption at even moderate activity levels.