Hi and thanks for using 2CarPros.com The first thing I recommend is to pressure test the system and see where the leak is coming from. Here are general directions for doing this:
https://www.2carpros.com/articles/radiator-pressure-test
If you determine the water pump is the issue, and there is a good chance, here are the directions for removing and replacing the pump. Just FYI, these cars are very particular and touchy. Make sure to follow the directions I provided. Additionally, I have attached several pictures which correlate with the directions.
2004 BMW 330Ci Coupe (E46) L6-3.0L (M54)
Vehicle  Engine, Cooling and Exhaust  Cooling System  Water Pump  Service and Repair
SERVICE AND REPAIR
Removing and installing complete water pump (M52 / S52 /M52TU/ M54 / M56)
Remove alternator drive belt, refer to Engine, Cooling and Exhaust - Engine - Drive Belts, Mounts, Brackets and Accessories - Drive Belt - Service and Repair - Procedures See: EngineDrive BeltService and Repair
Note: M52/S52 The water drain plug is located on the exhaust side between cylinders 4 and 5 in the engine block (illustration).
M52TU / M54 / M56 The water drain plug is located on the exhaust side on cylinder 2 in the engine block.
Drain and dispose of coolant.
Installation:
Replace seal.
Tightening Torque, refer to Specifications - Mechanical. See: Specifications
Vent cooling system and check for leaks, refer to Engine, Cooling and Exhaust - Cooling System - Service and Repair - Procedures. See: Service and Repair
Release belt pulley.
Release water pump.
Tighten two screws (M6) into thread of water pump and water pump out of timing case.
Installation:
Replace O-ring and coat with coolant as anti-friction agent.
I hope this helps you. If you have other questions or concerns, feel free to let me know.
Take care,
Joe
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Wednesday, May 30th, 2018 AT 7:54 PM