It is indeed 2.2 - 2.7 bar shown on the side of the door, depending on the load. However, the tires I've got on are of no known brand and pretty useless...3.6 is the lowest I can have in them if I want to avoid a "boat" feeling. Based on your info I'm sure the issue can be reduced heavily if the tires and suspension parts are upgraded/changed. It's on my loooooong to do list.

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BMW X5 E53, 4.8iS - 2005
Professional Stereo/Nav with DSP (modified BM54 module) - Converted to Eonon GA5166X with Reverse cam
4-Corner Air Suspension - Converted to BC Coilovers