With an engine that size most 540i's will be autos and steptronic autos at that or are you meaning paddle shift gear changes on the steering wheel.
Auto transmissions are not for the diyer.
BMW are as much use as a chocolate teapot when it comes to autoboxes.
Sure they can unbolt if from the car and fill and drain it with oil but that is it. I believe at an Inspection II they check the fluid level in the tranny but then they are also meant to change the differential oil also but I have never seen or heard of this getting done.
Take it to an Automatic Transmission Specialist for a full fluid change, filter change and all the other tweaks that they will do on your autobox. An auto box service will set you back about £120 -£150 inc vat. Half of which will be the cost of the oil!
The ZF boxes fitted to Beamers are reasonably strong units. Do a search on here for automatic transmissions to show the faults that have happened to them. I had to pay £700 to get mine fixed.
I am 99% sure my next E39 will be an auto.
HTH
Andrew
Edited by Andrew Rolland