This is one of the reasons I like running ... I was just commenting on FB that our "storm total precipitation map" starts six days ago, yet I've been able to run completely in the dry on four of those days so far and it's looking very promising for today. Haven't seen my bike in a while, though. 
Best thing to do with wet shoes of any kind is stuff them full of newsprint as soon as you get home. An hour or two later, pull the insoles out and replace the wet newsprint. (If they don't deliver free ad papers in your area any more, yes the paper CAN be spread out and dried for re-use.
) They will be as close to dry as they're going to get by morning.
Speed comes from what you put behind you. - Judi Ketteler