Carol, not her real name, described how he started molesting her when she was five and continued the abuse for four years.
She told the Argus newspaper the abuse took place whilst Bell was the Bishop of Chichester.
Her mother worked for the diocese and Carol often went to the offices with her.
"I went for weekends and school holidays, usually for two or three days at a time, sometimes a week," she said.
"He used to say to her, 'well I'll take Carol and I'll read her a story while you get on with your work'."
"It was whenever he got a chance to take me off on my own."
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She originally wrote a letter to Bishop Eric Kemp in 1995 but her complaint was only responded to by the current Archbishop of Canterbury Justin Welby when she wrote to him in 2013, and this led to her receiving £15,000 compensation and an apology from the Church.
She told the newspaper: "When things started to be more open that's when you feel you can say something. You thought about saying something for years but then you thought 'no'. And then when you do, and not a lot's done about it, you shut up again.
"It's something that lives with you for the rest of your life. It never goes away. You can push it, for a while, and then something, you either read in the paper or see on the television, and it comes back again."
The matter was reported to the police in 2013 when evidence was reviewed by the Crown Prosecution Service and was deemed to be sufficient to have warranted the former bishop's arrest and interview if he had been alive, leading to the compensation claim.
The Bishop of Chichester praised the victim for speaking out about the abuse she suffered.
Dr Martin Warner issued a formal apology in October and has now issued a fresh statement.
He said: "It is testimony to her courage and integrity that the survivor who brought the allegations against George Bell has been prompted to speak out.
"My hope is that the telling of her story will contribute to her sense of being heard by those within and beyond the Church who are willing to listen with an open mind and respond with compassion and clarity.
"The presence of strident voices in the public arena which have sought to undermine the survivor's claims has added in this case to the suffering of the survivor and her family.
"To that extent it is not surprising that she felt it necessary to take the courageous decision to speak out in public and reveal the personal details which the Church could not.
"Words of apology written in a letter can never be enough to express the Church's shame or our recognition of damage done.
"However, the apology that I made on behalf of the Diocese of Chichester is genuine and a sincere expression that lessons are being learnt about how we respond to accusations of abuse.
"In some responses to the George Bell case, and to the original statements from the Church nationally and locally in the diocese of Chichester, we have witnessed shocking ignorance of the suffering felt at many different levels by victims of abuse."
