'an old-fashioned' is a type of a cocktail ,that is a mix of sugar ,bitters than an alcoholic drink
( whiskey, brandy etc..) with citrus rind and he is listening to the music of 'bumblebees', there is an Irish music band called so, but relatively new if you are talking the thirties, so it might be a modern band,in all cases he is listening to music not real bees ;)