Word Detective was one of the few to take a stab at it and said:<1951 “The Act of Drinking: .. . to swill one down; to ‘TIE ONE ON.’”—‘Western Folklore,’ X, page 82:>
_______________________“The one clue we have about the origin of ‘tie one on’ only deepens the mystery. The OED compares ‘tie one on to the British slang phrase ‘tie a bun on,’ also meaning ‘to get drunk.’ . . . . no one seems to have the vaguest idea where ‘tie a bun on,’ which appeared around 1901, came from, or what a bun could possibly have to do with getting drunk.”
Here is what I was able to piece together, which looks to me to be the ‘likely’ source of the expression. A search of various “tie on’s” revealed the expression TIE A BAG ON: “phrase [1940s and still in use] (U.S.) to get drunk ‘tie one on’ + ‘bag.’” But it would seem that Cassell’s has his ‘tie a bag on’ etymology backwards here since they have under TIE ONE ON: “verb [1950s and still in use] (U.K./U.S. to be drunk),” which says that ‘tie a bag on’ came first followed about 10 years later by ‘tie one on.’
But still, what was it that was being ‘tied on.’ Checking the various slang meanings of ‘bag’ (and there are many), I found the following in Partridge’s A Dictionary of Slang: “BAG: a pot of beer . . .—1887 (‘Saturday Review,’ 14 May. Cf. ‘get/put (one’s) head in a bag,’ to drink: id. and nautical (ibid) probably from horses nose bag [[or feed bag]].”
So there we have it, and it doesn’t appear all that mysterious to me (in spite of what the OED and Wordwizard say). The 'bag' in question probably originated as the ‘feed bag’ which one ties on a horse and which later probably became associated with a drunk, drinking out of a pot of beer as if it were a feed bag tied around his neck – good visual. I also found confirmation of the ‘bag/drinking’ connection in the expression IN THE BAG (not the familiar ‘certain, sure,’ one which derives from ‘in the game/hunting bag’): “[1940s and still in use] (originally U.S.) drunk; thus HALF IN THE BAG (1920s) and HAVE A BAG ON (1940s and still in use). But less than 10 years later folks probably decided that that the slightly shorter, and definitely smoother sounding ‘tie one on’ tripped off the tongue a bit more easily than the older version and so today ‘tie one on’ it is, mostly!
Ken G – January 23, 2004