I have asthma, too. Just take your medication (especially your inhalar before you go running) and you should be fine. Unless you have bronchitis or pnemunia then asthma is really only a petty excuse to be lazy.
Just run a mile every day and try to up your time from your normal time once every week. (12 minute mile jog on Monday - Friday, try to beat that Sunday or something).
You're not going to get better unless you push yourself. The heart is a category 3 muscle and needs to be worked regularly for improvement.