One huge difference between your car and your wife's is that her MINI is running an optical MOST bus. Your e39 runs a wired I-Bus. Also, in 2003 Bluetooth was not so common, at least not to OEMs. Meanwhile, the iPod could not connect to OEM radios until BMW introduced the first adaptor in June 2004.
So her MINI was designed with Bluetooth and iPod in mind, but your car not at all.
The adaptor introduced in 2004 should work in your vehicle. It is not officially supported by BMW, and may experience some minor glitches, since it was never tested for that application. You might occasionally lose the iPod mode, or have to remove/replug the iPod, but I would be shocked if it didn't work at all. At the website listed below, you can pick vehicles by year. You'll have to pick the vehicle that has the radio most similar to yours (post a picture?)
Unless you have navigation, the radio cannot show any text. And, there is no way to select artists etc, because the I-Bus does not offer such a feature. Therefore, all that was available was to make 5 custom "BMW1" "BMW2" etc playlists available from the 6 preset radio buttons (the adaptor is faking like it is a CD changer, basically). The 6th preset uses the entire iPod as a huge playlist, so you can put it in random mode and keep skipping until you hear something you like, then un-random. Or, you can unplug the iPod, select something, re-plug it, and a handy Resume Play feature will keep playing your selection.
Installation is not for the faint of heart. You need to remove the radio, disconnect the battery, and remove and swap some pins into the connectors on the back of the radio. A special BMW workshop tool is needed to remove the pins, unless you can find some kind of a tube of the exact diameter to push in the locking tabs. As I recall, this harness swap could be faked with some Scotchloks or similar-not a great solution, but if you can't get that tool, maybe your only option unless you pay for dealer install.
If you want to run satellite radio as well, then a long audio wire has to be run clear to the back of the car. If you have a DSP system the you need a special model which has an optical output.
Look at BMW North America
and good luck.
P.S. There are a number of aftermarket units out there. However, BMW has a HUGE number of requirements for devices on the bus, including hardware and software, which they do not release. It is definitely possible to hack a device to WORK on the bus, but absolutely no guarantee it might not cause problems like interfering with bus communications or keeping the bus awake. Try those at your peril.
P.P.S. Or, you can do what I did: tear out the crummy OEM radio, and put in an iPod-specific Alpine radio. Threw out the lousy factory DSP amp and "sub"woofers, never looked back since. Maybe cheaper than the BMW unit installed at a dealer.