Doris Day in THE GLASS BOTTOM BOAT (1966).

Jennifer Nelson and Bruce Templeton meet when Bruce reels in her mermaid suit, leaving her bottomless in the waters off Catalina Island. She later discovers that Bruce is the big boss at her work (a research lab). Bruce hires Jennifer to be his biographer–only to try to win her affections. However, there’s a problem: Bruce’s friend General Wallace Bleeker believes that Jennifer is a Russian spy, and he has her placed under surveillance. When Jennifer catches on…Watch Out.