Changing an adult disposable diaper in public is pretty easy and all you need to do is either slip a new diaper down your pants or put the new diapers in a back pack and bring them inside the store to the restroom or into the restroom where you plan to change the diaper.
When I go into a store and need to change my diaper in the stores bathroom I usually slip the new diaper down the front of my pants and that holds it in place until I get into the restroom and then I just go into a stall and pull down my pants and then remove the old diaper.
Then I put the new diaper against the wall of the stall and back myself into it and then pull it up into place and tape it shut.