Green’s Dictionary of Slang

a drunkard; a heavy drinker; see also later boozer n.

1607		T. Walkington Optic Glasse of Humors 13: Most of them are the greatest bouzers, and bussards in the world: they had rather drinke out their eyes then that the wormes shoulde eate them out after their death. [Ibid.] 24: For drinkes, wee must not like bowzers carouse bowle after bowle.
c.1615		‘The Famous Rat-Catcher’ in Rollins Pepysian Garland (1922) 63: He was so braue a bowzer, that it was doubtful whether He taught the Rats or the Rats taught him to be druncke as Rats togeather.
1793		Sporting Mag. June II 164/2: The bowser of good ale is the picture of health.
1800		‘Jack at the Windlass’ Garland of New Songs 6: When he took on his knee Betty Bowser, / And he talk’d of her beauty and charms, / Cried I, ‘which is the way to heaven now, sir,’ / ‘Why you dog,’ says the Chaplain, ‘her arms’.