Proper bust? A lie -- it's false! (8)
I believe the answer is:
suitable
'proper' is the definition.
('suitable' can be a synonym of 'proper')
'bust? a lie it's false' is the wordplay.
'it's false' is an anagram indicator.
'bust'+'a'+'lie'='bustalie'
'bustalie' is an anagram of 'SUITABLE'.
(Other definitions for suitable that I've seen before include "Appropriate, befitting" , "Fit" , "qualified" , "In character" , "Convenient" .)