Wow I am surprised no one has responded to this yet. Well really you have sports specific conditioning. Biking and running have seperate levels of conditioning. I suck ass at running but on a bike I am strong. Any conditioning I do on biking helps minutely in running and any running I do helps minutely in biking. This is my opinion and really doesn't have a scientific basis. This is just something I have realized in the past few years of exercise.
Heart lungs do require a recovery time but because of their constant use (similar to calves and abs for general muscles) their recovery time is incredibly fast. I think the only time you have to worry about this kind of recovery is if you are doing a 'split'. Morning run and afternoon bike for example.