Wash the car on the lawn. Use a trigger nozzle hose and/or bucket. There are even waterless spray-and-wipe car wash products, but they tend to be costly.
Wash the car less often. Everyday dust and dirt won't harm anything if it collects for a little while.
Wash the car at a car wash. Car washes may use less water than you can use at home. Car washes also collect and filter the waste water appropriately.
Use environmentally friendly cleansers. This will enable you to reuse waste water from washing to water the lawn or garden.