The most common and most likely answer to this crossword clue is the 15 letter word NEOCONSERVATIVE
N
E
O
C
O
N
S
E
R
V
A
T
I
V
E
Buddy explains!
The straight part
We know that "with Bush’s persuasion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case with bush’s persuasion = neoconservative.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 NEOCONSERVATIVE mean?
NEOCONSERVATIVE noun- A supporter of neoconservatism.