A fluid dispensing system (30) includes a pump body (41) configured to couple to a container (37). The pump body (41) defines fluid inlet openings (50) and a pump cavity. A shroud cover covers the pump body to draw fluid from the container. An inlet valve (51) allows fluid from the container (37) to enter the pump cavity through the fluid inlet openings (50). A plunger (56) is slidably received in the pump cavity, and the plunger (56) defines a fluid passage with a dispensing opening through which the fluid is dispensed. A shipping seal seals the fluid passage during shipping to minimize leakage of the fluid during shipping. An outlet valve is disposed inside the fluid passage to minimize the height of the fluid between the outlet valve (90) and the dispensing opening so as to minimize dripping of fluid from the dispensing opening. The pump body (41) includes a venting structure to normalize the air pressure inside the system.