Yes having a swimming pool will increase your water bill.
The amount your water bill will increase when you have a swimming pool depends on the size of the swimming pool and how many gallons of water that your swimming pool holds.
A smaller swimming pool will use less water and a larger swimming pool will use more water.
To fill up your swimming pool it might add an additional $50.00 to $200.00 for one month's water bill depending on how many gallons of water that it takes to fill the swimming pool with.
You usually only have to fill the swimming pool up once and as long as you use chlorine in the swimming pool the pool water should not need changed until the next season.
If your swimming pool is an above ground permanent swimming pool or an in the ground swimming pool then your homeowners insurance also goes up and your property taxes increase as well.