Coolant light goes on and off while driving continually replacing water

Your car has a coolant level sensor. When the car is cold(1st thing in the morning)check the coolant level. The float should be floating if it isn't top it off to get the float floating. Have you had the cooling system pressure tested yet? The e46 3 series can develop leaks in the Reservoir, Radiator, Thermostat, and Water pump. It all needs to be looked at closely.