I try not to put myself in those situations. Since I started wearing regularly I haven't had the problem. Before I started wearing actual diapers, I had 2 very bad very public leaks. Once was in the mall food court. I had ot walk all the way out of the mall with soaking we pants. Everyone saw and knew. This taught me first and foremost that you need to wear adequate protection at all times. A dry bulky diaper is less embarrassing than a thin diaper that's leaked and running down your legs.
Now, I wear appropriate protection. A Northshore Supreme Lite will last me until lunch time easily. That's 5-6 hours of wear under normal fluid intake. I can either adjust my intake or wear one of my overnight diapers instead if I think I'm going to be gone longer than that or think I won't want to or be able to change. I also always use the toilet any time I change my diaper. I won't strain myself buy generally I can always pee a decent amount when I try.
If I go out to a movie or something, usually dinner is first. After dinner I'll just go change even if my diaper is only a little wet. I'll also use the toilet then just to make sure my bladder is empty before I diaper up again. Usually for the movies or a show, I'll wear a night time diaper too just for added confidence of making it all the way through. Same protocol for sports games, museums, etc.
When I go skiing, I wear an overnight diaper (Abena L4 or similar) with a full Abri Let Maxi booster. Trying to change a diaper in a ski lodge is a nightmare so I just go all Super Diaper on it. I was at Attitash this weekend and skied all day Saturday and Sunday without having to change once all day. By the end of the day though, my diaper weight like 5 lbs haha.
I haven't yet found myself in a situation where I truly couldn't change if needed. I haven't been on a long flight since being incontinent yet so that will be interesting when the time comes. I'm kind of a big dude so changing in an airplane bathroom seems unlikely. Next year we're supposed to go to Tonga (where my wife's family is from) and that's a loooong flight (boston to LA, LA to Sydney, Syndey to Tonga). Obviously chances to change on the layovers but the LA to Australia leg will be a challenge.
SLOMO makes a good point, in that you should avoid waiting until you're near full capacity. Once I figured out my incon "style" it became easier. My accidents are always gushes/floods, but not always full bladders. I might leak anywhere from 3 to 12 ounces at once. A 12 ounce flood is a big one. If I have more than 2 big floods, I change. Even if my diaper can handle 85ounces i Know that A) ISO capacity isn't 'real' as much of the diaper isn't used and B) there's no prize other than ebmarrassment if you push it. Like SLOMO, I change with usually at least 20% unused practical capacity. I haven't had a noticeable leak in ages doing this.