Ahhh...the magic of "tri-shorts."

They make special shorts for triathlon that are quick drying, slightly padded and won't give you sores going from swim to bike from the moisture. There's not a whole lot of padding there (it looks like a piece of felt), but it's enough to help on the saddle. I was surprised how comfortable I was in my trishorts the first time I biked in them. There also isn't thick padding that you even notice it while running like you would in bike shorts. Tri-shorts are made of a more bathing suit type material and often have mesh sections as well to help with drying.

I have a pair from Hind that I really like.
BK