Any plan that involves more than a few sentences will fail.

Just ask directly if she want to go for a drink someday. Don't compliment her, because that's kind of old.

Having worked in a supermarket, I don't remember any cashier dating with a customer, even though most of the cashiers spent their time talking about sex and flirt during their break. I unhappily think this is not a good situation to start any kind of relationship, but good luck anyway :)