Nope, just remove the dirt from your feet, put on your shoes and helmet and start cycling! Tri shorts are designed with a very thin chamois that dries quickly, so you can wear them for the whole race. You're asking the wrong person for brand advice, though--I own one pair that I wore for both races last year. They seemed to work fine but I have no idea what brand they are. TE has a good variety of tri shorts, so if you have a brand of bike shorts you like already, see if they make triathlon clothing as well.

One thing I learned was that it's not worth it to try to dry yourself off too much. I'm paranoid about blisters, so in my first (pool) tri I dried my feet off carefully and tried to dry my body off as well to avoid getting too chilly, but that slowed me way down in transition. So for my second tri I tried to get smart and use baby powder on my feet (the normal trick is to have a dishpan or bucket of water and dip your feet in them to remove the gunk after the swim, but I always use baby powder to get rid of sand from my feet at the beach, so I thought it could work here too), which would remove the debris and keep my feet dry during the rest of the race. I shouldn't have bothered--as soon as I was on my bike the water from my shorts and top dripped down my legs and got my feet as wet as if I hadn't dried off at all, and again, powdering your feet takes longer than a quick dip in a water bucket or a squirt from a water bottle. In both cases, I was pretty dry by a couple of miles into the bike portion, so my attempts at keeping my feet dry weren't worth the effort!