"I think Billie is the kind of girl who would let her hips swing loose"

When Judy Holliday stated "I think Billie is the sort of woman who would let her hips swing loose", she was likely referring to the manner in which Billie brings herself. To "let her hips swing loose" suggests a particular casualness and freedom in motion, which suggests that Billie is an easygoing and positive woman who doesn't take herself too seriously. It also suggests a specific sensuality, as the hips are typically thought about an especially attractive part of the body. Overall, Holliday's comment recommends that she admires Billie's carefree energy and possibly even envies her capability to be so free-spirited.