BMW 325ci 2001 model with just over 121000 miles on it. This car had been eating oil but no leaks under the car/anywhere in the engine bay. I gave it an oil change and after a few weeks of driving the oil light came on and was very low on the dipstick so I topped it up and checked again a week later and noticed that it had lost quite a bit of oil in a week.
Can't find a leak anywhere in the engine bay or under the car but noticed that the oil cap both times had a little bit moisture on like drops of water/tiny little bit of white and I mean tiny. What could it be?
Did you look at the rear of the engine? these car had problem with leaking valve cover gasket. It leaks on to the heat shield above the exhaust manifold and it will burn off before you see it.
FWIW. My BMW X5 with the N52 engine had an oil leak at the valve cover gasket. It was hard to spot, because the oil was burnt on to the side of the engine / valve cover.
The N52 is the successor to the inline-6 petrol engine on your generation of BMW 3 series, so I suspect that may be the cause of oil loss.
My engine is the m54
M54 is the predecessor to the N52. Very similar engines.
Possibly the valve cover gasket could be your problem.