I knew I had read about the BSA origin of Beemer somewhere....

This is from wikipedia. No guarantee as to accuracy.

The term "beemer" started as a pronunciation of the acronym "BMW," adapted from the early-20th-Century British pronunciation of BSA (as "beeser" or "beezer"), whose motorcycles were often racing BMW's. Over time, the term became closely associated with BMW motorcycles.
The term "bimmer" was later coined to refer (exclusively) to BMW automobiles. As such, use of the word "beemer" to refer to a BMW automobile is frowned upon by BMW enthusiasts, because it is the term used for motorcycles. Although the distinction is somewhat arbitrary, to this day, the media, movies, and most people still use the term "beemer" to refer to the automobiles due to their ignorance of this fact. Interestingly, in the German language, the correct pronunciation of the term "bimmer" is "beemer."

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