Madame Muchmoney's Granbull is a Granbull owned by Madame Muchmoney. When it was still a Snubbull, it had a recurring gag in season 3 which included it biting Meowth's tail. Its trademark items were the ribbons on its ears.
It used to live with Madame Muchmoney and lived a pampered life, but never had any real freedom. Upon seeing Meowth's tail, it ran after Team Rocket for the sole purpose of biting his tail because it loved to bite tails. After Madame Muchmoney promised to give it more freedom, it went back home with her.
As a Granbull
Still feeling something was missing, it ran off again after Team Rocket. After several appearances, it appeared one last time in The Trouble With Snubbull, where it evolved into Granbull and returned home with its owner, who had been looking for it.