Several jokes in this episode refer to Bull's puppet as being made of wood, like a traditional ventriloquist dummy. It is obviously made of foam and felt and not wood at all, like a Muppet.
The ventriloquist dummy that Bull uses during this episode is the same one that he inspires a professional ventriloquist to make in Bull's image during the first episode of this season. It is conceivable that Bull received a duplicate one from the ventriloquist as a thank-you, or purchased one himself from the same source.