If you're in a public restroom and change a dirty diaper you can just roll the diaper up and place it directly into the trash can.
I would recommend carrying plastic bags to place the dirty diapers in and then tie the bags up in case you can't place the diaper into a trash can right away.
Then you can place the dirty diaper inside a backpack until you can find a trash can.
But if there is a public trash can nearby just either throw the dirty diaper directly into the trash can or place the dirty diaper into a plastic bag and tie it off to reduce the smell.
But most people just place the dirty diaper directly into a trash can and never worry about it as many people do just throw dirty diapers into the trash can and it's okay to do so because that's what the trash cans are for are trash and dirty diapers.