From the Super Mario Wiki
Barney Bubble is a purple ball that wears blue shoes. Two appear in the original Super Mario World 2: Yoshi's Island, in the Monkey's Favorite Lake level, while the remake, Yoshi's Island: Super Mario Advance 3, adds two more in the World 6 Secret, Endless World of Yoshis, during the forest area.
Barney Bubbles quickly run back and forth. They cannot be eaten and can only be defeated by being hit with an egg. When stomped on, they merely produce bubbles that Yoshi can then eat and spit out himself for a variety of uses. Bubble Dayzees produce these same kind of bubbles. Their name is a reference to Barney Rubble from The Flintstones.
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