Men often pee off the side of the bike when they are racing, they just pull it out of their shorts and kind of shift their weight to the side and pee. I've seen it often, mostly when I have been driving wheel support. The last time I drove wheel support I was following the young masters (35+) and they were gentlemenly enough to take a pee stop off to the side of the road. I averted my eyes as I stopped the wheel truck behind them! I guess I'm shy.

I have never tried to pee on the bike, sounds nasty, but I have many times arranged for a stop on the side of the road to pee. It's just part of the game.