Abstract: A mop bucket assembly for use with a wringer device and a mop includes a container having partition elements dividing the container into compartments. A first compartment contains a liquid for rinsing the mop head after mopping. A second compartment receives a liquid extracted from the mop head by the wringer device. A fourth compartment contains a cleaning solution. A housing is received in a third compartment and a flexible bladder is disposed in the housing and is in fluid communication with the fourth compartment. The flexible bladder contains a supply of cleaning solution. Liquid extracted from the mop head by the wringer device flows through an opening in one of the partition elements and places pressure on the flexible bladder, causing the cleaning solution in the flexible bladder to flow into the fourth compartment to maintain a desired level of cleaning solution in the fourth compartment.