Persistently preoccupied Bess does wrong (8)
I believe the answer is:
obsessed
'persistently preoccupied' is the definition.
(I've seen this before)
'bess does wrong' is the wordplay.
'wrong' is an anagram indicator.
'bess'+'does'='bessdoes'
'bessdoes' with letters rearranged gives 'OBSESSED'.
(Other definitions for obsessed that I've seen before include "with bee in her bonnet?" , "With compulsion" , "Persistently preoccupied" , "With mind continually occupied, abnormally focused" , "Being excessively concerned with something" .)