The most common and most likely answer to this crossword clue is the 7 letter word TAURINE
I've seen this crossword clue in The Guardian
T
A
U
R
I
N
E
Buddy explains!

The straight part
We know that "Bully" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bully = taurine.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 TAURINE mean?
TAURINE adjective- Pertaining to a bull; bull-like.
- An amino-sulfonic acid, NH2CH2CH2SO3H, that has regulatory functions in mammals.