The most common and most likely answer to this crossword clue is the 13 letter word MAGNILOQUENCE
I've seen this crossword clue in The Times
M
A
G
N
I
L
O
Q
U
E
N
C
E
Buddy explains!

The straight part
We know that "bombast" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bombast = magniloquence.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 MAGNILOQUENCE mean?
MAGNILOQUENCE noun- The quality of being magniloquent; pompous discourse.