A bag container dispenser includes a bag container. The container is formed of resilient material and has a bottom, a top, first and second sides, a front, a back and a removable access panel. The access panel has a top segment that includes a portion of the top and a connected front segment. The front segment has a height that extends from the bottom to the top. Stacked bags are sized and shaped to fit within the bag container. Each of the bags has a front wall, a back wall, an open top and a closure mechanism. The bags are dispensable from the container through an opening provided by removal of the access panel which may have a removable cover. A dispenser rack has a horizontal platform sized and shaped to support the bag container. Peripheral guards extend upward from the platform and constrain movement of the container during dispensing.