Bishop having responsibility for extra payment (5)
I believe the answer is:
'extra payment' is the definition.
(I've seen this before)
'bishop having responsibility' is the wordplay.
'bishop' becomes 'B' (abbreviation used in chess).
'having' means one lot of letters go next to another.
'responsibility' becomes 'onus' (onus is a duty or responsibility).
'for' acts as a link.
(Other definitions for bonus that I've seen before include "Additional payment as reward for service" , "Extra payment, may be performance-related" , "Extra dividend" , "Extra pay, perhaps at Christmas?" , "Extra payout" .)