E.,
My trick when we are out and about on the weekends with our daughter is to announce that Mommy has to go potty and take her to the bathroom. Once we are in the restroom I tell her that she gets to go first. We have never made a big deal out of visits to a public toilet. I just tell her we are going. She has been in plenty of restrooms even before we started potty training, so it wasn't a scary place to her. I have to help hold her on the potty so she doesn't worry about falling in. Last weekend I got her to the restroom by telling her that she could ride the elephant. We were at the Renaisance Festival with her cousins.
The most important tool I have found while we are out is to make the time to take her to a bathroom whether I need to go or not. As adults we get so focused on getting so much done in a limited amount of time that we forget that little bladers need relief sooner. Restroom stops may slow me down, but at least I'm getting stuff done. Good Luck!
J. N.