There you have it! If you have to pee a lot whilst riding, then you are not working hard enough - so pedal harder, pee less.
I live in a hot climate. I also sweat a lot even in a gym,I always thought if you don't sweat it's not a workout. I tend not to pee but after suffering kidney stones , the doctor told me, "if you need to pee, pee". For me it's not worth holding it in. The pain of kidney stones is not to be snuffed at. I would rather go thru anything else again but that. The doctor said, "stay hydrated by drinking plenty of water throughout the day and drink cranberry juice, it helps".
I just love being on the bike on a hot day as the ambient wind is so refreshing. You are in fact with the bike being air conditioned.
I was cycling with my brother in Córdoba last year. We decided on a long distance, the temperature was an insane 42c, no matter how much you drank it was impossible to hydrate sufficiently and I didn't want to pee. By the time we got back to the car I felt good until I got off the bike, then I thought I would have to go to hospital, being too cold is perhaps better than too hot. So that's why they have siesta's in Spain.
Some long distance marathon runners poop too. So it's an interesting idea using some tubing. I bought some nice shoes recently, the tube would have to be sufficiently aimed as not to spoil them.