I can't comment on water bill increases because we're on a well. Only the tiny population in the town has "city water" and sewer.
I use a doggie pool (like a kiddie pool but smaller diameter and not as deep), a 70 gallon rubbermaid tank, a 50 gallon rubbermaid tank, a 8 qt dabbling bowl and a many quart bowl.
I refill the quart bowls twice daily. The rubbermaid tanks get changed when either 1) the water smells, 2) the water is green or 3) the water is no longer see through.
The doggie pool gets refilled when it is no longer see through or when the ducks splash too much water out. It's just barely deeper than their legs are long. Some times that means its changed daily but usually I can get a few days out of it.
I reuse all that water to water the yard, plants,garden, trees, etc.
I raised my ducklings inside and while they were little I noticed that they wasted less water and made less water mess the more water options I gave them. When they were growing up I had1 water pan for dabbling/splashing for each duckling plus 1 for flock games plus 1 that was only able to be used for drinking.