I found this little rendention on the net thanks to the BMW Car Club of BC:
"Bimmer vs Beemer
Enthusiasts vs others
Definitions:
Bimmer - proper accepted slang for BMW cars. Most people don't know this.
Beamer/Beemer - proper accepted slang for BMW motorcycles. You will hear this term used incorrectly by many people.
Bummer - When you get a speeding ticket.
Bitter - Another German car. Very rare; hand built.
So just why is a BMW car called a 'bimmer' not a 'beemer' or 'beamer'?
The answer in part lies in knowing some BMW history and what came first.
All real BMW enthusiasts know that BMW got a big start on two wheels, what many call the real BMWs.
In those days, BMW motorcycles were quite active in racing, and one of their competitors at the track was often the BSA bikes.
Well as things would have it, a track slang developed, and the BMWs were usually referred to as 'beemers' and the BSAs were referred to as 'beesers'.
So, of course for any true enthusiast, there is no way that a BMW car could be called a 'beemer', so they were called 'bimmers'.
Unfortunately, in the US and Canada, and perhaps other countries, there was a time (kind of still is) where for various reasons, a BMW owner was considered an upwardly mobile person, and of course due to the fun in driving their BMWs most all of them had big grins on their faces.
Hence it is little surprise that the non enthusiast types out there incorrectly labeled BMW cars and their owners as 'beamers' or 'beemers'. "