I couldn't ride at all if it wasn't that I use a steroid inhaler every day as prescribed. I guess it would depend on how severe your asthma is when you exercise. Maybe you should consult a family doctor who can test your respiratory function (usually a quick test in the office), and then refer you to a specialist for more extensive testing if necessary. I know many people don't like to take medication, but the thing is, with asthma, if you don't treat it, you risk worse breathing problems later on in life due to the remodeling of the airways that occurs over time due to the inflammation in the airways.
But I wouldn't look at asthma treatment to improve performance... only to prevent asthma attacks while doing it.