"Bimmer" usually refers to cars while "Beamer" refers to bikes. At least that's the general consensus on the forums.
I think the distinction has lost any meaning outside of the most ardent fans. In the west there are few BMW motorcycles and so Beamer generally applies to both.
"Beemer" for bikes and "bimmer" for cars is certainly what I have observed among BMW enthusiasts. At least on the US west coast.
'Bimmer' I was aware of too, I didn't realise there was a distinction between the cars and bikes, I always assumed it was just regional differences!
I think you meant to take a more holistic view, and wonder, are we both right? ;-)