Well, ours uses water heated by our solar water panels and runs on electricity from our photovoltaic panels. Both systems have already paid for themselves. We even have a year's supply of dishwasher detergent passed on by a neighbor who was moving out of her house.
So... for us it's just the cost of a few gallons of water.
I've read that dishwashers can get the job done on less water. In our case, two adults who don't use many plates or bowls at home, we only run a couple loads a month. I think we'd use a lot more water doing a few dishes in the sink at a time.