The most common and most likely answer to this crossword clue is the 4 plus 4 letter word GOLF BALL
I've seen this crossword clue in The Times
G
O
L
F
B
A
L
L
More clues leading to the result GOLF BALL
Buddy explains!
The straight part
We know that "bouncer dispatched by club" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bouncer dispatched by club = golf ball.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.