We've got a couple of local riders on randonneuring rides with similar issues. What they do is stop every 29 minutes or whatever it takes. Some are more discreet about it, some less so. It's part of life, you're not the only one. Riding in rural areas helps. If you're careful, you can stop and pee while still straddling the bike. And with those local riders, usually, it's a couple of stops near the first of the ride, then less often thereafter.
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"be careful this rando stuff is addictive and dan's the 'pusher'."