A package including a fitment for dispensing a liquid from a flexible bag is disclosed. The fitment is secured to the bag and includes a compressible bulb and a piercing member that are coupled together. The fitment is configured such that when the bulb is first actuated, e.g., pressed, it causes the piercing member to pierce through the wall of the bag so that the contents of the bag can be dispensed through an outlet port of the fitment. In one embodiment of the fitment a portion of the piercing member is permanently located within the bag after first use and a valve is provided to open and close the outlet port thereafter. In another and more preferred embodiment the piercing member is extended into and out of the bag to dispense the contents of the bag through the outlet port, without necessitating use of a separate valve to open and close that port.