I have a 2001 3.0i as well. I searched extensively trying to get a definitive answer on this when I decided to change the fluid.

Short answer is that DEXRON VI is what BMW currently specifies. More info below, from the notes I took at the time:

5L40-E/GM5 (A5S 390R) 5-speed auto transmission made by GM
A = Automatic (vs. S = Standard)
5 = 5 forward gears
S = top gear is overdrive (vs. D = top gear is direct drive)
390 = Max input torque rating in Nm
R = manufacturer is Hydramatic (GM Powertrain - Hydramatic in Strasbourg, France) (vs. Z = ZF or G = Getrag)

ATF capacity: 10.1 quarts/9.1 quarts (capacity for the X5 is 0.5 liters/quarts greater than for the 5 series with the same AT). But another BMW doc says "5L40-E/GM5 (A5S 390R) FOR X5 - WITH TORQUE CONVERTER - 9.6 LITERS - WITHOUT TORQUE CONVERTER - 8.6 LITERS"
Blue sticker on bottom of AT pan says use only BMW 83220024359
which appears to be Texaco ETL 8072B, which was Dexron III
superseded by BMW 83220397114, which is Dexron VI
So as of Dec 2014, the correct replacement fluid is Certified Dexron VI


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Also - note that the answer for the 3.0i is completely different from what it would be for the V8's. Completely different transmissions.

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2001 X5 3.0i, 203k miles, AT, owned since 2014