Possible Clues:

• Suit named for an atoll
• Skimpy two-piece swim wear
• Brief bathing costume
• A follower ones taken family to see bathing suit
• Two bits? That's not much to put on here
• Tan line cause
• One might just as well have nothing on atoll
• Bathing suit for the atoll
• It has two pieces, top and bottom
• Skimpy two-piece swimsuit