A dispensing system including a cap that is capable of securing the dispensing system to a bottle filled with a formula, wherein the cap is configured to retain a metered dose of the formula, a shaft in fluid communication with the cap, an accordion bladder inside the cap, wherein the accordion bladder includes at least one opening, one or more bellows, and a stopper, a distributor nozzle in fluid communication with the shaft, and an outer nozzle covering the distributor nozzle and configured to dispense the formula.