Almost count on bachelor (6)
I believe the answer is:
barely
'almost' is the definition.
(thesaurus)
'count on bachelor' is the wordplay.
'count' becomes 'rely' (I've seen this before).
'on' is a charade indicator (letters next to each other).
'bachelor' becomes 'ba' (the qualification: Bachelor of Arts).
'rely' after 'ba' is 'BARELY'.
(Other definitions for barely that I've seen before include "Not quite" , "just a short while before" , "Just about, nothing to spare" , "By a small margin" , "as Godiva rode?" .)