The most common and most likely answer to this crossword clue is the 4 plus 4 letter word SICK BEDS
I've seen this crossword clue in Financial Times
S
I
C
K
B
E
D
S
Buddy explains!
The straight part
We know that "Where you might find Dick and Bess, out of sorts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where you might find dick and bess, out of sorts = sick beds.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.