BMW was born as the merger of two companies, BFW (Bayrische Flugzeug Werke - Bavarian Airplane Works) and Rapp Motoren Werke. The Rapp logo was a circle with a thick black border and a white interior. The border had RAPP in white letters, and the interior had a silhouette of a chess knight. (Although Rapp was the founder of the company, der Rappe is the word for the chess piece.)
White and blue are the state colors of Bavaria, they appear on the flag and on the state seal, and they derive from the coat of arms of the Wittelsbach family, the hereditary rulers of Bavaria for over 700 years. According to the state song, the white-blue lozenge pattern represents the sky over Bavaria.
The BMW roundel was first registered in October of 1917. There was a ban on the use of any symbols of the government or the royal family in trademark logos. And yet, the company management clearly wanted to link the company and its products to the state it was named for. So, they inverted the order of the white and blue areas so as to remain distinct but mistakeably similar to the state symbol, and, using the pattern of the Rapp logo, they put it in the center, with BMW in the black border.
I found this image of the Rapp logo:
