The most common and most likely answer to this crossword clue is the 4 plus 5 letter word BUCK TEETH
I've seen this crossword clue in The Times
B
U
C
K
T
E
E
T
H
More clues leading to the result BUCK TEETH
Buddy explains!

The straight part
We know that "these sticking out of mouth/the bucket" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case these sticking out of mouth/the bucket = buck teeth.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.