The most common and most likely answer to this crossword clue is the 6 letter word SHREDS
I've seen this crossword clue in The Daily Telegraph
S
H
R
E
D
S
Buddy explains!

The straight part
We know that "bits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bits = shreds.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 SHREDS mean?
SHREDS noun- A long, narrow piece cut or torn off; a strip.
- In general, a fragment; a piece; a particle; a very small amount.