The most common and most likely answer to this crossword clue is the 6 plus 7 letter word SPEECH BUBBLES
I've seen this crossword clue in Financial Times
S
P
E
E
C
H
B
U
B
B
L
E
S
Buddy explains!
The straight part
We know that "an they bear what characters say in storyline?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an they bear what characters say in storyline? = speech bubbles.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.