this reminds me of a similar puzzle with the car which has no front window and no roof and the question is wether to go fast or slow to get least rain.
if you would go (theoretically) with infinite speed, your time would be 0 and you would get no rain. therefore going faster is the better option. now in this case you have the ability to get no rain while going slow as well. but my feeling tells me that this wont matter to much. my first guess is: keep pedaling.
but then again the answer could be that sometimes pedaling fast and sometimes rest would balance to regular pedaling. so it wont matter what you do. ill think more