My initial issue for a class 1 involved a number of hoops to jump through. I can't remember what my % is, but it shows a modest improvement after a broncodilator. For the initial I had to see a specialist (who asked the same questions my aviation doctor did then charged $300), have a spirometry test, and then have CAA's doctor make a conclusion. I was given a cert but with multiple requirements (carry inhailer when PiC etc), some of which have been relaxed over the years.
This is for mild but definitely present asthma.
My only advice is to find a doctor with their own spirometry machine to save $, have your medical history to give the doctor, and do your best to have your condition under control and be otherwise healthy. Also if you haven't done any work towards a CPL yet wait until you've got the cert in your hand. It could be a long process! Sorry for not having numbers, a call or an email to info@CAA might get you in contact with Dougal or an underling. No real risk doing so in my opinion, who knows maybe just a vague concept like "under control" rather than a firm cutoff applies.