Bill Cosby was so famous back in the day, and appeared to be a mentor and friend to black entertainers starting out in the business. His image was squeaky clean. Why wouldn’t she have trusted him?
Well, she was a young, good-looking girl trying to make it in showbiz; I’m sure she was familiar with the casting couch. By telling her to bring her daughter with her for the first visit, Cosby was probably trying to give her the impression that he was safe and not interested in making a move on her.