A fluid supply system includes a fluid supply subsystem and a fluid bottle subsystem. Pressurized air or other suitable gas supplied to the fluid supply system causes a piston housed within the fluid supply subsystem to translate toward the fluid bottle subsystem, thereby sealing an interface between the fluid supply subsystem and the fluid bottle subsystem. The pressurized air or gas also causes a fluid (e.g., a coolant or rinse liquid) within the fluid bottle subsystem to flow through the piston and out of the fluid supply subsystem where it may be used. The fluid supply system enables the fluid bottle subsystem to be installed or uninstalled from the fluid supply subsystem without requiring bleeding off of the air or gas supplied to the fluid supply system and/or without requiring the fluid bottle subsystem to be rotated or twisted into place relative to the fluid supply subsystem.