My wife had terrible asthma when I met her, 53 years ago. She'd been living with a smoker and she's allergic to the smoke. The smoker was gone, but not the asthma, still has it. Yes, absolutely do NOT wait until you have symptoms. Take a hit off the Albuterol every time before you do something which might trigger the asthma. Ideally, you never want to feel "tight". Toughing it out is exactly the wrong thing to do. Do it before you have symptoms. Put it in your helmet or bike shoe. You doctor doesn't know crap about it. He's dead wrong. Albuterol is harmless, asthma is not.

My wife has chronic asthma, meaning she'd have problems with it even if she didn't encounter an agonist, thus she'd have trouble all the time if she didn't take medication. She has to use a fluticasone/salmeterol inhaler daily as well as the albuterol before aerobic activity. She's been doing this for 50 years with no adverse effects, nor has her asthma gotten worse, if anything it's better.

Personally, I'd change doctors. Wrong about one thing, maybe wrong about many things.