I'm thinking about getting a road bike. I can wear diapers underneath bike shorts.
Don, I can tell you about my situation although it isn't really the same as yours since I don't have the bowel problems. I have a dripping problem and can get through most days with no protection, but exercise seems to aggravate the dripping and my bike rides last 1:20 to 1:30, so I always have a strong urge to go long before finishing. I also refuse to dehydrate myself in an effort to stay dry. As the urge to pee increases, the dripping becomes dribbling and squirting, especially when I hit bumps and since I can't hold much anyway I'm going to be wet one way or another by the time I finish.
I've tried diapers underneath and by folding the waist down about two inches I can hide most of it, but sometimes they ride down as I pedal and I find myself with an inch or so of white diaper showing above my shorts. Also the bulk shows although long shirts help a bit. After a bit more than a year I've discovered the best thing for me in the summer is to wear black bike shorts made of that Spandex material and just let it flow. It just doesn't show on the black very much and dries very quickly. It saves a diaper as well.
In cold weather I wear an Abena pull-up (my standard diaper I buy by the case from XP Medical) with a pair of black sweatpants on the outside. I wet less in the winter since I drink less water, but you'd have to look very closely to see anything.
Just my experience. Good luck with the biking.