The Rev Prebendary Kay Garlick, at the opening meeting in York, acknowledged the outcome would inevitably bring "hurt" to some members.
But she said the Synod should present a model of how Christians who disagree can respect and care for each other.
Some 1,300 clergy have threatened to leave the Church over the issue.
Ms Garlick, from Much Birch, Herefordshire, told the meeting: "The business committee [of the General Synod] have striven... to allow Synod to rise to the challenge of presenting to those who follow our progress a model of how Christians can disagree in love, respect one another's sincerity and care for one another as we try to discern God's will for our Church."
The Bishop of Manchester, the Rt Rev Nigel McCulloch, will lead a debate on Saturday on a report outlining the options open to the Church of England in proceeding with women bishops.
Consciences
Traditionalists want the legal right to opt out of the supervision of a woman bishop, and into the care of a male alternative.
The Synod has already agreed in principle to ordain women as bishops.
BBC religious affairs correspondent Robert Pigott says it faces an awkward decision about how to treat traditionalists whose religious consciences will not allow them to serve under a women bishop.
He says Anglo-Catholic Anglicans argue that Jesus chose only men to be his immediate 12 apostles, the men who were given leadership of the early Church.
They point out that an unbroken chain of male bishops has led the Church since then.
Our correspondent says they believe that a man ordained by a woman might not be properly ordained, and might not in reality be a priest.
Such a suggestion is strongly rejected by women priests and many others in the Church.
Meanwhile, a traditionalist Synod member has accused officials of suppressing his call for an explicit policy of converting people of other faiths, including Muslims.
Paul Eddy's motion was backed by about a quarter of the Synod, but officials say the agenda was too crowded.
The Fellowship of Confessing Anglicans - the international alliance of traditionalist Anglicans formed in Jerusalem last week - has made the duty to evangelise other faiths one of its key policies.
Thanksgiving
The General Synod will also hear a presidential address on Saturday from the Archbishop of York, Dr John Sentamu.
He opened the meeting with a series of prayers including thanksgiving for the 60th anniversary of the founding of the National Health Service.
He also prayed for the Church throughout the world, and for Zimbabwe.
Ugandan-born Dr Sentamu, who cut up his clerical dog collar in protest at the regime of President Robert Mugabe, said: "We pray for our brothers and sisters in Zimbabwe. God bless Africa, especially the people of Zimbabwe. Guide her people and guide her leaders and give her peace in Christ our Lord."
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