Possible Clues:

• A follower ones taken family to see bathing suit
• Skimpy bathing costume or Pacific atoll
• It may be worn on a beach
• Two-piece wear
• It has a top and bottom
• Swimwear of family in British Isles?
• Usin' a cycle to go over island, one now uninhabited
• Small two-piece bathing costume
• Swimsuit style
• Cycle endlessly in a scanty costume