A medicine bottle is formed with a neck that defines an opening and a closed bottom opposite the opening. A closure element is engaged with the neck to block the opening, and the closure element is formed with a fluid passageway. A fitting is positioned in the fluid passageway. The fitting is configured for receiving the hub of a needleless syringe, and a tube which has a proximal end is positioned in the bottle with the proximal end in fluid communication with the fitting. The tube also has a distal end disposed near the bottom of the bottle. Consequently, the syringe can be engaged with the fitting for drawing liquid from the bottle into the syringe without inverting the bottom of the bottle over the neck of the bottle, even when the bottle is nearly empty.