There are different paint codes of Alpine white, you can find yours by looking on the lower part of the strut tower (on my E32 at least). Make sure you supply the 3 digit code as well.
Then, within that single paint code are a variation of different paint samples that were produced just by the imperfection of maintaining identical paint mixes from the factory.
Alpine White 146
Alpine White II 218
Alpine White III 300
check here Automotivetouchup.com Touch Up Paint, Aerosol Spray Paint and Touchup Paint Accessories | AutomotiveTouchup | 888-710-5192
As I do not know your built year, I have selected a 1994 E34 and the result is:
BMW paint code # 300 Alpine White III/Alpinweiss III
where I live there are car accessory shops like in the U.S. Autozone etc, they mix the color based on the original paint number, so I just tell them BMW paint code # xy and they can mix it for me, as touch up or also in a spray can.