You should probably talk to a doctor about getting an inhaler. It is common to take a rescue inhaler before strenuous exercise. If your doctor says that isn't an option, ask about other cardio options. I'm sure they'd be happy to help.
With an inhaler, your workout schedule should be the same as normal. see c25k or other starting programs.
I've seen many team mates be successful with asthma. I don't know how bad theirs is compared to yours, but it is at least a somewhat common problem.