Get a Kill-A-Watt or similar and measure it.
Usually dishwashers are hard-wired, so a kill-a-watt isn't really an option.
The dishwasher manual, of all things, might give you some useful information. But even without that, we can put an upper bound on how much the dry cycle costs. Your dishwasher won't draw more than 15A max on a 120VAC line, so the maximum it could every possibly draw at one time would be 1800W. Let's say the dry cycle takes 30 minutes. That gives you 900 watt-hours, or about 1kWh. For us, that's about $0.11 worth of power. Keep in mind, though, that that's a very high estimate. I would guess that it draws less than half as much current.
Is your wife's time worth less than a nickel per load of dishwashers?
FWIW, I run the dishwasher without the heated dry, and just leave it open for a while when it's done.