With my luck I would try it and get someone who starts yelling at me in front of a bunch of people. I DO embarrass easily! That's the hard part not knowing, what might happen. But I can see where the bag or purse might make a difference or help some. Atleast if you have the bag an emplyee could always say they didn't see a dog if it's "hidden" in a purse thus avoid getting into troublefor not saying anything but I guess it's harder to say "Dog, what dog?" if it's sitting in a cart looking at you.
Maybe they are less luckily to say something with the purse. I can't even take my Missy to see my grandmother because dogs are not allowed in her trailer park, not even for a visit. My sister tried to sneek in her small dog once and my uncle (Gram lives with) said someone saw it an complained. I keep thinking I am going to bring Missy to see her and when my Uncle says No Dogs! I am going to tell him she's a cat!!! And hope he doesn't notice the difference