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. In two embodiments the fitment is configured so that the piercing member pierces through a wall of the bag to dispense the bag's contents through an outlet port of the fitment. One of those embodiments includes a separate valve to open and close the outlet port. Another embodiment does not include a separate valve to open and close the outlet port. A third embodiment makes use of a fitment connected to a filling gland of the bag and which is in communication with the interior of the bag. That third embodiment includes a frangible seal forming part of the fitment and which is pierced by the piercing member to dispense the liquid from the bag.