The most common and most likely answer to this crossword clue is the 6 letter word SNORER
I've seen this crossword clue in Financial Times
S
N
O
R
E
R
More clues leading to the result SNORER
- Tin, about to be returned, containing yellow kipper we hear
- A number more angry about someone noisy in bed
- Not best companion for quiet night out?
- Welcoming back to prison, more angry one might cause disturbance at night?
- Relatively irritated about new annoying bedfellow?
- One making noises during long sermon, for example, and not during short sermon
Buddy explains!

The straight part
We know that "annoying bedfellow" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case annoying bedfellow = snorer.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.