I write from the Finnish perspective, so take this as a travelling with incontinence tip.
I tend to use university and library toilets. They are usually free to use: other places here usually have toilet-fees and most bus-station or metro (in the capital) restrooms are icky. However, I luckily very rarely have to change as I usually can make it to the toilet in time, or then I take the liberty to urinate in a bush or ditch. Illegal, yes, but if one is discreet and does not do the business on the street, no one really gives a flying finch. And I don't like emptying my bladder into a diaper if the problem is that no toilets are around but perfectly fine bushes or woods are. I have a health issue and when you've gotta go you gotta go.
Talking about discretion, for me the problem is usually the tape-sound (opening and readjusting for using a toilet), but I've never had anyone say a single word. It is also possible to mask the sound. If other people are urinating outside the cubicle or washing their hands, they probably donät hear the tab crackling.
I've learned to change and re-adjust in very limited space and prefer to do it standing against the cubicle wall. Sometimes disposal is easy, there are often bins inside the cubicles as they also contain sinks and paper hand-towels, but of course throwing a used diaper away if one has to carry it into out of the cubicle can be tricky. I usually roll & tape it into a tight bundle, listen carefully for a quiet moment and just very quickly drop it into the bin. Train toilets are easy for disposal when travelling by rail, but the standard toilets are crammed and often rather messy, so it is best to find the train's disabled WC which has enough room for a wheelchair and for changing children's diapers, so they suit incontinent adults' needs very well. All trains, at least on the long distances, have these facilities.