Rebuff making bachelor hurry away (5,3)
I believe the answer is:
brush off
'rebuff' is the definition.
(synonyms)
'bachelor hurry away' is the wordplay.
'bachelor' becomes 'B' (abbreviation e.g. BA=Bachelor of Arts).
'hurry' becomes 'rush' (synonyms).
'away' becomes 'off' (synonyms).
'b'+'rush'+'off'='BRUSH-OFF'
'making' is the link.
(Other definitions for brush off that I've seen before include "Rejection, dismissal" , "Curt rejection" , "Snub" , "Casually dismiss" , "fox's condition after hunt" .)