The most common and most likely answer to this crossword clue is the 9 letter word CORNFLAKE
I've seen this crossword clue in The Times
C
O
R
N
F
L
A
K
E
Buddy explains!
The straight part
We know that "a bit of breakfast" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a bit of breakfast = cornflake.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 CORNFLAKE mean?
CORNFLAKE noun- A toasted flake of maize used as breakfast cereal.