The most common and most likely answer to this crossword clue is the 5 letter word WAHOO
I've seen this crossword clue in The Times
W
A
H
O
O
More clues leading to the result WAHOO
Buddy explains!

The straight part
We know that "burning bush" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case burning bush = wahoo.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 WAHOO mean?
WAHOO noun- Acanthocybium solandri, a tropical and subtropical game fish.
- The winged elm, Ulmus alata.
- Euonymus atropurpureus, an eastern burning bush.