The most common and most likely answer to this crossword clue is the 3 plus 4 plus 7 letter word THE MIND BOGGLES
I've seen this crossword clue in The Times
T
H
E
M
I
N
D
B
O
G
G
L
E
S
Buddy explains!
The straight part
We know that "that's bizarre!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that's bizarre! = the mind boggles.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.