The latest edition of "The Piping Times" has a discussion on the meaning of the title of this tune, and brings up the following clues.
An early manuscript (circa 1866) of the tune has the title written as 'The Black Baird' - the old Scots word for 'beard'. However there is another option.
The Scots word for barley is 'bere' and, in 18th and 19th century documents, it is usually spelt thus, but sometimes 'bear' (pronounced 'beer'). An old popular variety of this grain had black beads on the heads and was known as 'the black bere'. There seems little doubt that the word 'beer', meaning ale, comes from 'bere' meaning barley. Perhaps, therefore, the tune should be called "The Black Beer" (i.e. porter or stout)?
It used to be customary, in some regiments, for the pipers to play this tune when entering the barracks after a route march or a day's manoeuvres. At a certain point, the whole battalion gave a great roar, possibly in anticipation of foaming pints in the mess !
Either of the above options would seem to be a better explanation of the title than with an animal which has been extinct in Scotland for a thousand years and more.
Willy nilly, it is a great tune to play and to march to.