Itsy-bitsy comes from the word "ici-pici", which is used in Hungary to tiny, small things. It was taken into the US (to Holywood) by a Hungarian film director in the early 20th century. Then he used it in everyday life and stuck to others. This is the one and only Hungarian word that was adopted to English.
In Hungary you can also say: "iciri-piciri" (this means smaller than "ici-pici").
"Volt egyszer egy iciri-piciri házacska..."
Means "There was an itsy-bitsy small house..." in a famous Hungarian tale.