A fluid dispenser is described that includes a dispenser, a cap, and an insert. The dispenser is flexible and includes a body portion and a cylindrical mouth portion extending from the body portion. The mouth portion has an opening defining a lip. The cap is operable to engage the mouth portion of the dispenser, said cap has an aperture therethrough operable to dispense a fluid stored within the dispenser. The insert is sized for placement within the opening, between the mouth portion and the cap and includes a substantially solid plug having a first and a second axial hole therethrough, a first reed valve operably attached to the plug to close the first axial hole from an outside of the dispenser, and a second reed valve operably attached to the plug to close the second axial hole from an inside of the dispenser.