In one aspect, a water supply system for a waste disposal may include first and second supply conduits fluidly connected to separate water supplies, with the first supply conduit having a first discharge end and the second supply conduit having a second discharge end. The system may also include a disposal conduit fluidly connected to the first and second supply conduits. The disposal conduit may be spaced apart from the first and second conduits such that an air gap is defined between an inlet end of the disposal conduit and the first and second discharge ends. The inlet end may be configured to receive water expelled from the first and second supply conduits. Moreover, an outlet end of the disposal conduit may be configured to be in fluid communication with an inlet of the waste disposal such that water directed through the disposal conduit is received within the disposal.