In one aspect, a water supply system for a waste disposal may generally include a supply conduit configured to be fluidly connected to a water supply, wherein the supply conduit has a discharge end. The system may also include a disposal conduit in fluid communication with the supply conduit and a supplementary conduit in fluid communication with a storage tank containing an additive fluid. The supplementary conduit may be configured to supply the additive fluid into the flow of water directed through the disposal conduit to create a water/additive fluid mixture within the disposal conduit. Moreover, an outlet end of the disposal conduit may be configured to be in fluid communication with a disposal inlet of the waste disposal such that the water/additive fluid mixture directed through the disposal conduit is received within the waste disposal.