I am almost sure that 84116945940 will not work. There was a period of time in model year 2004 cars where bluetooth modules were installed that had the bluetooth logo on the sticker and even had pairing code on them but the bluetooth circuitry did not work. BMW even gave people a card with the bluetooth pairing code when they bought their car but later had to admit that their cars didn't have bluetooth. Bluetooth was not functional in the TCU until model year 2005 cars (build dates 9/2004 and later) There is a BMW service bulletin on this. For bluetooth you need a TCU with a build date after 9/2004 (i.e. 2005 model year cars).
All that said there are CDMA (USA) and GSM (Euro) TCU modules. In the US only CDMA bluetooth modules work, even though you'd think for the bluetooth it wouldn't matter whether it was CDMA or GSM. Also we have both CDMA and GSM networks in the US (Verizon and AT&T for example) but BMW uses the Verizon CDMA network for their TCUs. I have no idea what the situation is in Australia for this aspect. Sorry.
If you can get TCU from a 2005 model or later E46, X3 or Z4 it should work. These are all iBus cars (not the brand new Z4 hard top convertible). After the upcoming X3 revision, all BMWs will be MOST bus based.