Many folks are following the Tour de France for the first time this year. The number one question I get about cycling is: how to cyclists pee during a race stage which lasts five to six hours long? I answered this one a long time ago but I thought it was worth repeating.
There are two options. One: jump off your bike and run over to the side of the road like your average club cyclist and do your business. If you're lucky, one of your teammates will stick around and help to ride you back to the peloton. If you do it early in a stage the peloton will probably take it easy and not attack while you're answering the call. Sometimes you may have to answer a higher calling, in which case you may have to stop and knock on a door of a house somewhere along the road. Luckily, your average French family will likely consider it an honor to have a Tour rider's derriere gracing their toilet seat.
The other option, if the race is tight, is to just pee from your bike. Maybe a teammate will keep a hand on your back seat and keep you rolling so you can just turn the opposite way and pull your bib down and keep that outside leg down. After all, you don't want that any corrosive liquids touching your precious Campagnolo or Shimano components.
I've never actually tried to fire while on the move. In the intense heat of the French countryside during the Tour, one usually doesn't have to worry about over-hydrating; it's dehydration that's the constant enemy. But the second you get off the bike, that huge surplus of liquid you've built up keeps you running to the bathroom every fifteen minutes for a few hours.