Billy (Big Blue House)

From Muppet Wiki

Billy is a bunny boy who appears in the Bear in the Big Blue House episode "A Trip to the General Store". He lives with his mother Bonnie, and their home was damaged by flooding from the storm in "Welcome to Woodland Valley." Many of their possessions were damaged as well, and Billy lost some of his favorite toys. He accepts an invitation to play at the Big Blue House. Billy is generally seen wearing a cap.