The acronym standing for Bavarian Motor Works, obviously, is BMW and consequently is the marque found on the products of said company.
Let's analyze that for a moment...
The first letter...."B."
Normally pronounced Bee.
Hence the more commonly seen "Beemer" when using the common slang terminology regarding these particular automobiles.
They are Bee-Em-Double-Us. Not Bi-Em-Double-Us.
Considering it is slang in the first place I would suggest there is no "correct" way to spell it.
Thank you for your cooperation and understanding.
/rant.