It follows a complaint by journalist Peter Hitchens about the revelations.
The force said it was apologising to Barbara Whitley because police did not contact any living relatives of the bishop to let them know an inquiry was to be made public by the Church.
It said it was not apologising for the investigation or the statement itself.
In a letter to Mr Hitchens, Det Supt Jeremy Graves, head of the force's professional standards department, said the force would apologise to Ms Whitley.
"The distress caused to Barbara Whitley is of course regrettable and I know that Katie Perkin [head of corporate communications] plans to personally write a letter of apology to her," he wrote.
He continued: "With hindsight the matter could have been managed more sensitively but it was complicated by the fact that the release was generated by the diocese with whom we should have been working more closely."
He said the issue of the impact of media statements on people connected with suspects was difficult to manage.
But he said: "I am satisfied there was no intention to confuse or cause distress."
Carey criticised over abuse-claim bishop
The battle for a bishop's reputation
In October, the force issued a statement that said there had been an allegation of serious sexual abuse by the late Bishop Bell in Chichester in the late 1940s and early 1950s.
It said police investigated the circumstances, with the full co-operation of the victim and diocese, but further action was not possible because Bishop Bell had died 57 years earlier.
The statement went on to say: "The information obtained from our enquiries would have justified, had he still been alive, Bishop Bell's arrest and interview under caution, on suspicion of sexual offences."
The Diocese of Chichester has not yet commented to the BBC.
Sussex Police is to "apologise" for distress caused to the niece of Bishop George Bell by a media release about alleged abuse by the cleric.