OK I will throw a wrench in the works...I was brought up in upstate NY,
where Bimmers were people that worked at IBM.

In alt.autos.porsche The Dead Senator <deadsenator@hotmail.com> wrote:

I had to go look it up... it appears Beemer can be used for both, but Bimmer
is for cars only... why?  I have no idea... anyway, I mispelled it either way.

http://www.boston-bmwcca.org/reference/Bimmer-Beemer.aspx  says;
"... A Very Highly Placed BMW Spokesperson sent me the following (reproduced
    here with permission).

   While I can't point to any official document that supports this, my
   understanding of the origins are as follows.

   The term Beemer was first used with motorcycles. Back when British bikes
   dominated the market and BSA was a well-known marque, riders referred to
   them as Beezers -- a way to say the letters BSA as if it were a word.

   BMW riders said Beemer as a way of saying BMW as a word. This was long
   before the popularity of BMW cars, so whenever the term Beemer was spoken,
   it referred to the motorcycle. In theory, one could apply Beemer to either
   cars or bikes since it is only a reference to the name BMW. In fact some
   folks do call BMW cars Beemers.

   When the cars became popular, many people referred to them as Bimmers as
   well as Beemers. I don't know why this was adopted instead of simply using
   the existing Beemers.

   But generally speaking, one calls the bikes Beemers and the cars Bimmers.
   While it would be ok to refer to a car as a Beemer, it doesn't seem
   appropriate to refer to a bike as a Bimmer. ..."