The most common and most likely answer to this crossword clue is the 3 letter word JAG
I've seen this crossword clue in The Times
J
A
G
More clues leading to the result JAG
Buddy explains!

The straight part
We know that "Drinking bout" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drinking bout = jag.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does JAG mean?
JAG noun- A sharp projection.
- A part broken off; a fragment.
- A cleft or division.
- A medical injection, a jab.
- To cut unevenly.
- To tease.
- Enough liquor to make a person noticeably drunk; a skinful.
- A binge or period of overindulgence; a spree.
- A fit, spell, outburst.
- A one-horse cart load, or, in modern times, a truck load, of hay or wood.
- A leather bag or wallet; (in the plural) saddlebags.