Throw in bush — half sorry about that (10)
I believe the answer is:
contribute
'throw in' is the definition.
(thesaurus)
'bush half sorry about that' is the wordplay.
'half' suggests halving the letters.
'sorry' becomes 'contrite' ('contrite' can be a synonym of 'sorry'**).
'about that' is an insertion indicator.
'bush' with half the letters taken is 'bu'.
'bu' put inside 'contrite' is 'CONTRIBUTE'.
(Other definitions for contribute that I've seen before include "Chip in - supply" , "pay" , "Furnish" , "Donate" , "Give money etc for a cause" .)