She made her first appearance when she was seen flying above The Bathhouse soon after the very first nightfall in the movie. She appears to show some characteristics of Yubaba; their faces are similar in shape and features.
Later in the film, Yu-Bird was transformed into a very small creature, resembling a fly, after Zeniba made her first appearance to Chihiro, Boh, and Haku. Boh takes a liking to Yu-Bird after their transformation; they can both be seen throughout the later parts of the film riding on Chihiro's shoulder and playing together.
It is not made apparent in the movie if they had a positive relationship prior to being transformed or not.