I get one - not all the time and I cannot ever predict when it will happen, but after a long, hard ride (nothing like a TT or anything like that, though - usually one with a lot of climbing that makes me breathe hard). I get a cough that can last as much as 24 hours. The best way for me to describe it is that I have a tickle way down in my throat that won't go away. If I try to take a deep breath, I cough! It is almost like my chest is constricted slightly and that causes the tickle. I do not have exercise-induced asthma....though I was mis-diagnosed as having it a few years ago.
"When I'm on my bike I forget about things like age. I just have fun." Kathy Sessler
2006 Independent Fabrication Custom Ti Crown Jewel (Road, though she has been known to go just about anywhere)/Specialized Jett