Hail charge being added to bill (6)
I believe the answer is:
accost
'hail' is the definition.
(I know that hail is a more specific form of greet)
'charge being added to bill' is the wordplay.
'charge' becomes 'cost' (I've seen this in other clues).
'being added to' says to put letters next to each other.
'bill' becomes 'ac' (short for account).
'cost' put after 'ac' is 'ACCOST'.
(Other definitions for accost that I've seen before include "Approach or hail boldly" , "Approach boldly or aggressively" , "Meet and greet" , "Approach boldly and speak to" , "Make bold approach to" .)