From Disney's Hollywood Studios Wiki
Bean Bunny is a Muppets Character who first appeared in 1986 as the star of the TV special The Tale of the Bunny Picnic. Though at the time of the Muppet attractions at Disney's Hollywood Studios he was not considered a major character in the Muppet world, he was featured in every one of the Muppet attractions.
 Studios Reference
Bean Bunny has the distinction of being the only Muppet character to appear in all three forms of Muppet Puppetry featured in the park, including standard puppetry on the screen of Muppet*Vision 3-D, as well as in Animatronic form in the audience, and in Meet and Greet form in Here Come the Muppets, and Muppets on Location: Days of Swine and Roses.
On the small screen, In 1989 to be exact, Bean joined the cast of The Jim Henson Hour, appearing in both the control room and "televised" portions of the MuppeTelevision segments. Although his fellow Muppets often found him to be insufferably cute, the MuppeTelevision ratings were never higher than when the station featured sex, violence, and/or Bean Bunny. An animated version of Bean Bunny was introduced during the seventh season of Muppet Babies, and a pre-teen Bean would later be featured as part of the Muppet Kids series.
Featuring Bean in all the Muppet attractions was a push to make him more popular from his Jim Henson Hour Days, unfortunately, it didn't catch on.
Bean's only prominent role in a Muppet movie was in The Muppet Christmas Carol, where he played the young boy who fetched a goose larger than he was for Scrooge on Christmas morning. In subsequent appearances on Muppets Tonight, Muppets from Space, It's a Very Merry Muppet Christmas Movie, and The Muppets' Wizard of Oz, Bean was relegated to the background and became a routine target of Muppet violence, a fact that Brian Henson makes note of on the Muppet Christmas Carol DVD commentary: "Inside the Muppet Company, we love to hate Bean Bunny."