if yamato doesn't become a pirate she doesn't get one
Not necessarily. Simply being Kaido's daughter may be enough to land her a bounty. The One Piece world is one big dictatorship headed by the World Government. They don't really care if you are a pirate or not. If they don't like you, and you sail across the sea, you're a labeled a pirate and they will issue a bounty for you.
EDIT: Also, they were doing experiments on Kaido for some reason, they could issue a bounty to capture Yamato in order to resume experiments on her instead. Kaido and Yamato aren't humans, apparently, based on what Kaido said to Yamato.