The most common and most likely answer to this crossword clue is the 6 letter word ALOHAS
A
L
O
H
A
S
Buddy explains!

The straight part
We know that "Byes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case byes = alohas.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 ALOHAS mean?
ALOHAS noun- Good wishes, love.
- An utterance of aloha (see Interjection, below).