When a master plumber is self-employed and works solo out of his house or apartment, how do these people deal with throwing away customers old toilets and water heaters since they don't have a dumpster at a shop?

each city or town is different as far as disposal.
one city near me allows the homeowner to purchase a sticker from city hall and leave the toilet or water heater out front and the trash collector take it away.
i have always discussed with the property owner just what they wanted to do. some said to leave the item and they would dispose of it. others have said they would pay me to dispose of it.

bottom line is they are many different options.

Where I work most of the places that sell water heaters will take the old one back, then haul it to a scrap yard. If I get stuck with one I'll take it to the scrap yard myself.

Toilets don't take up much space if you take a hammer to them.

In south Florida most cities or counties have what is called a bulk waste pickup. It is either scheduled like once a month or on demand where you are allowed say 2 bulk pickups a year and you call them to set up a pickup say 3 days out. It can be water heaters appliances furniture fences and tree cuttings. Do you have such services?

steve_g I took a hammer to a toilet ONCE. Never again. They do not break into smaller chunks. They shattered like glass with sharp pieces projectiles in all directions. Not fun.

sum,

place the bowl in a burlap sack THEN bust it up