To get diapers without my parents knowing I would take a backpack with me to a store and then leave my backpack on my bicycle and it would be empty.
Then I would go into the store and purchase the diapers in a package and then after paying for them and coming out the door I would place them in my backpack.
Then I would bring then in the house as normal and my parents would never think anything different.
Sometimes I would put something in it like a game, book etc and say I was going to my friends house and then just go to the store instead and stay out somewhere long enough to make it seem like I was visiting my friend and then return as normal with my backpack and diapers and could easily get them in the house without my parents knowing.
I would hide my diapers in my closet way back behind some stuff that my parents never went through.
When I wore diapers I would wear pants or shorts and wore them around my parents and they never found out.
As for disposing of the diapers I always took my own trash out and had my own trash can so that part was easy.
Some people have to sneak the diapers into a trash can or outside to dispose of or take them to another trash can.