A bottle comprises a container surmounted by a neck and an outer structural wall, having a membrane arranged on the inner surface to form a flexible pocket for containing product. A dispensing member intended to be mounted in the neck to be in communication with the container to be supplied with product. The member provided with a lower sealing crown arranged to be able to slide into the neck during mounting of said member, making it possible for excess air and product to be evacuated into an upper dead volume. The neck comprising a base having a narrow portion of which the inner dimension is such that, after the dispensing member is mounted, the lower crown comes into sealing interference on the portion of the membrane arranged in the region of said narrow portion so as to create a seal between the inside of said container and the dead volume.