If you said, "would you like to join me for dinner," that should not lead to them assuming you are paying. Only moochers would assume it.
So the question might then be ... "So what is the least expensive restaurant that I can take you to and get laid afterwards?" I suspect most women don't want honesty
I suspect this piece of advice will help you now and in the future: Never buy a woman dinner until after you've already had sex with her.
If your intentions are to keep paying for her food. BY ALL MEANS, PAY FOR HER FOOD, man. Don't be a CHEAPSKATE. If your intentions are to not pay for her foor, just be straight up with her and tell her you'd like to pay for your own. Don't be a hypocrite. Fixed. FOR ME, too. Damn you, cf'ers... always making me go home to eat out with my wife... AND THEN we'll go to a restaurant. HI-YO!!!!!
If you're paying to eat out, she's probably not that clean to start with. And you might get a side order of crabs by mistake.