Asthma and hyperventilation are not the same thing or have anything really to do with each other. I've done both. Asthma may be what the OP is referring to, just with the wrong terminology. The simple test is to take a deep breath and exhale hard. Do you hear a wheeze? If you do, asthma, if not, something else.

Something else:
When one goes really hard, one's energy production pathways change from aerobic to anaerobic. One can make energy without oxygen, but one's body doesn't seem to know that, and one feels one is in "oxygen debt" which one attempts to make up by breathing very hard and fast. One is actually trying to get rid of CO2. In this case, it's best to get control of the breathing by conscious deep breathing. When breathing in, start by inflating the belly, then the mid-chest, and finally the upper chest. Most folks, when they breathe hard and fast, only move the upper chest. This is incorrect. Slow the rate, and breathe deeply. This is the way to breathe when climbing.

One can also get in the habit of breathing every so many or even on each pedal stroke or footfall and then continue to breathe that rapidly even though one's effort has decreased as the road has leveled or one has stopped or whatever. This is true hyperventilation. It's unnecessary. You may feel dizzy. In this case, the simple solution is to gently stop breathing and just let your chest be quiet. The urge to hyperventilate will pass quickly if this is the cause.