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.

'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!

"Beemer" for bikes and "bimmer" for cars is certainly what I have observed among BMW enthusiasts. At least on the US west coast.