Costumes? Is this a movie? If you go to a department store, ask for bathing suits.
Just for interest's sake, Australians most commonly call these 'bathers', 'swimmers', 'togs', 'swimming costume' or 'cozzies', depending on where they live. I can't think of anyone who would actually say 'swimsuit'. I think this term varies around the world in English and that DL should be flexible in accepting different versions.