Number of calories burned are a measure of body weight, intensity of exercise, (measured by oxygen uptake), mode, and duration at a particular level. While your submaximal target heart rate may be the same on a bike as running it depends on the overall intensity and duration at a particular level of MHR. A metabolic ladder formula can help you figure out each minute what you burn at a particular stress level based on your weight.
A heart rate monitor can help measure your THR heart rate regardless of the mode of exercise, so that at 80% of your heart rate maximum you would burn the same per minute on a bike or a treamill if both where performed at 80%. Therefore you would need to figure out how many calories you burn at 80%.
Actually this can easily be done today on a treadmill that gives you heart rate and calories burned as long as you factor in your weight. They are pretty acturate.
An individual’s maximal heart rate doesn’t change. He or she may be working at different percentages of their heart rate but that doesn’t have an effect on one’s heart rate maximum.
To know how many calories are burned during a bout of exercise, one would need to know the metabolic equivalent of the activity the individual is engaged in. For the purpose of your question one would need to know the metabolic equivalent for cycling and running and also know at what intensities those activities are being performed.
Lastly, there is no correlation between the number of times the heart beats and how many calories are burned.
I hope this helps.