What is the best way to calculate my maximum heart rate?
I think on a bike it would be harder to reach max HR, but in running it is easy.  Find a hill (say 1/2 KM long) that is reasonably steep.  Warm up for 20 minutes of running, and start doing hill repeats.  Aim for a pace where you can do about 6 repeats.

Do the first three at increasing paces, and then for 4 and 5 start pushing to the max you can handle.  As jensgram said in his answer, push till you are about to faint, or vomit, or whatever your body uses to tell you to stop.

This is pretty darn close to your max HR.  At least functionally, before your body ups and quits on you.