A dispensing system including a cap configured to secure 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, a bladder inside the cap, wherein the bladder comprises one or more openings, and wherein the bladder is configured to lift to cover the shaft, a distributor nozzle in fluid communication with the shaft, and an outer nozzle covering the distributor nozzle and configured to dispense the formula.