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Trivia: Jodi Benson, who voiced Ariel in the 1989 animated movie "The Little Mermaid", appears in the live-action film as a marketplace vendor who offers Ariel a plate of food and a fork. In a reference to the original film, Ariel uses the fork to comb her hair. (01:20:30)
Answer: Her long hair covered her up.
There are a couple of shots after her transformation where you can tell she's no longer wearing her bra. However, I rewatched her transformation scene, and her bra is never seen coming off. It's just gone.