Say goodbye for a bit (4)
I believe the answer is:
part
I believe this is a double definition.
'say goodbye' is the first definition.
(I've seen this in another clue)
'bit' is the second definition.
(both can mean a piece of something)
'for a' acts as a link.
(Other definitions for part that I've seen before include "Separate - role" , "character on > stage" , "Element" , "Region" , "Piece, segment" .)