I got a tip for people with an ostomy who may choose to travel to Japan (or most Asian countries). There are no public garbage cans for the most part, so you may have to be creative in carrying your 'garbage' if you find yourself having to quickly dart into a public washroom to change your appliance.
And by the way...don't expect to see a toilet in the same fashion that you're used to here in the West, as most public restrooms in Asia are nothing more than a hole in the ground, and I do mean that literally.
If you're in a city, then the best place to seek out is a McDonald's as they will always have garbage cans where you can dispose of your 'garbage' and also decent washrooms to change in.
If you're traveling the countryside of any Asian country, you're gonna be hard-pressed to find anything that resembles a public washroom, so be prepared to be creative. I can usually change my appliance in about 45-60 seconds, so be prepared to rip off your old one and slap on a new one somewhere in the bushes so that you can quickly continue on with your journey.
On a side note, you will see fantastic washrooms in Japanese airports that often have signs that they have ostomate facilities inside. These are top-notch washrooms and even come with instructions....seriously folks, with instructions ;:)
Happy travels