I always assumed the pronunciation was just a regional thing. Everyone around here says "biker" but people I've spoken to around the country seem to say "basheer" more often.
I say Biker and it seems to be the most phonetic sense....But I believe its like Tomato Tamato etc different ways of saying it....but Bircher is DEFINATELY wrong because there is no "R" sorry mate
PS: The Search function would have brought you many of these phonetic debates to light