A mud bucket system including a base structure and a bellows with a longitudinal internal cavity, the base structure attached to one end of the bellows and a retention ring attached to another end, where the vertical movement of the retention ring lengthens or shortens the longitudinal internal cavity, and a method of using the system that can include coupling a mud bucket to a rig floor, raising a retention ring of the mud bucket, thereby elongating a longitudinal internal cavity of the mud bucket such that a connection of a tubular string is positioned within the longitudinal internal cavity, and unthreading the connection while the connection is positioned within the longitudinal internal cavity, where a tubular is connected to the tubular string at the connection and unthreading the connection disconnects the tubular from the tubular string and expels a fluid from the tubular into the longitudinal internal cavity.