Joanna Whibley, 48, who lives in Polegate, Sussex, told BBC Radio Four's Today programme that her son Kevin, 15, had been fathered by the Right Rev Roderick Wright during an affair which started after the bishop, then a curate, had instructed her in the Catholic faith and helped her through the trauma of a divorce.
Speaking on the verge of tears, she said: "I made up my mind that I must unburden myself and put an end to Kevin's feeling that he shouldn't even exist. Although Kevin knows it's his dad and Roddy knows he's his dad, he has been an absent father."
The bishop, 56, disappeared last week with Kathleen MacPhee, 40, a mother of three he had been counselling during her divorce, and later issued a statement resigning and apologising for the distress he had caused.
This statement was one of the reasons Ms Whibley went public. "Kevin feels his existence has been denied again. In Roddy's statement he apologised to his family. Perhaps he was referring obliquely to us, but I suspect he was referring to his other family. He apologised to the MacPhee family, but he didn't mention us."
Bishop Wright had panicked when he learnt she was pregnant, she said: "He offered no support ... [He] said he couldn't acknowledge being a father and if I forced him to, he'd go to Peru and I wouldn't see him again."
Kevin Whibley, who was also interviewed, said he had never made any secret of the fact that his father was a high-ranking Catholic priest. But he was bitterly disappointed in him. "I haven't seen him for more than two months in my life," he said.
Kevin said he had turned his back on his father: "I feel angry at the loss of a father and it's too late now. I don't even want him if he comes, it is too late.
"I'm glad when people ask me, because people ask me at school. I am tired of being awkward about answering.''
Father Tom Connolly, spokesman for the Catholic Church in Scotland, said that the discovery of Bishop Wright's earlier transgression had played a large part in the decision to accept his resignation last week.
"I was devastated when I learnt," said Fr Connolly. "I felt that his resignation was sad and sorrowful enough. But to learn of this was quite something.
But Cardinal Basil Hume, leader of Catholics in England and Wales, said he had had "no prior knowledge whatsoever on what has been disclosed about the bishop in the news this evening".
In a statement, he was said to be "shocked and saddened to learn of it. Clearly this does an enormous amount of damage, to the credibility of the Church, the credibility of individual priests trying to conduct their pastoral affairs, and to their counselling."
The revelations echo the case four years ago of the Bishop of Galway, Dr Eamon Casey who also disappeared from his diocese when news broke that an affair had produced a child.
At that time Peter Murphy was a 17-year-old high school student in Connecticut, in the United States, where he was living with his mother, Annie, a divorcee. The bishop was eventually tracked down to Ecuador.Reuse content