Yes there are 2 pumps.
Bmw e46 headlight washer not working.
The bmw e46 wiper and washer system consists of the following.
If you are 100 sure the fuse is ok then there is either a wiring issue or the pump itself is faulty as from memory you would still hear the pump try to work if it was just a blocked filter although it had been about 3 years since i ve had to mess about with washer pumps so can t remember 100 if that is the case.
Typically the problem is the contact point on the bottom of the bulb has oxidised or become fouled so that a clean connection no longer exists between the bulb and the lighting sensor.
Headlight washer pump in fluid reservoir if equipped.
Windshield wiper motor arms and blades.
Tailgate window wiper motor arm and blade sportwagon.
Washer fluid reservoir with fluid level sensor in engine compartment.
Windshield washer pump in fluid reservoir.