Ms Furness said the commission would hear evidence of Bishop Mulkearns' repeated refusals to deal with complaints of clergy abuse from a nun, a mother of a survivor and a fellow priest.
The commission has previously heard that Bishop Mulkearns was first told of Ridsdale's offending in 1975, but moved him to numerous parishes until Risdale was charged and later convicted of multiple child sex offences in 1993.
Sister Kathleen McGrath, principal of a Mortlake primary school where Ridsdale was parish priest, will tell the commission that after he was moved on, Bishop Mulkearns had "told them to keep matters very quiet".
After a number of parents complained to her that Ridsdale had molested their children, she asked Bishop Mulkearns if a public forum would be held.
"He replied that nothing would be done for the children because that would be admitting guilt," Ms Furness said.
During a five-minute meeting, the mother is expected to say, either she or her husband told Bishop Mulkearns: "We've got big problems in Mortlake."
"Before they said anything else, Bishop Mulkearns said: 'How am I to take the word of a child over one of my priests?' " Ms Furness said.
"[The mother] found Bishop Mulkearns' comments devastating. They made her think he was totally unsuitable to be in a position of leadership."
Father James Fitzpatrick, a former director of the Catholic Enquiry Centre in Sydney, is expected to tell the commission that he reported to Bishop Mulkearns in 1986 that a young boy had spent the night there with Ridsdale.
He had asked that Ridsdale be removed from the centre and will say "that the bishop was the person who was responsible ecclesiastically for Ridsdale and that whatever the bishop did with that information was his choice and responsibility," Ms Furness said.
The hearing continues.