In my experience, Italian "il costume" can often mean "bathing suit" or "swimsuit." The fact that it doesn't immediately offer "swimsuit" as translation help had been bothering me all through the clothing unit. I finally just tried "swimsuit" on this sentence and it took that as correct. Technically it's "costume da bagno," but I do remember hearing Italians at a beach in Italy using simply "costume" to mean "swimsuit" since it contextually made sense.
In America, "costume" usually has a narrow meaning, indicating clothing one would wear to masquerade as someone or something else. Thus, actors wear costumes; children wear costumes on Halloween (as they "dress up" as ghosts or witches or pop culture characters.) It is not applied to everyday wear and, usually, not to swim suits, technician uniforms, etc. So...what is the best Italian word for the American "costume?"