Bishop Libby Lane refused to answer whether she would marry gay people and said: "I want to play my part in the church continuing to struggle with what we do."
In an interview with the Guardian's Helen Pidd the bishop said: "I unequivocally want to be understood as saying that whatever my or the church's limitations are, I don't want them to be read by people who are gay to understand that that means that Christ is not for them."
The Church of England recently announced a number of 'shared conversations' in a bid to find a solution to the issue of how gay people are treated.
Discussions will include both liberal and evangelical Anglicans amid ongoing controversy sparked by the legalising of same sex marriage.
Asked if she would personally marry gay people Bishop Libby replied: "I want to play my part in the church continuing to struggle with what we do."
When asked again she refused to answer and said: "When I was ordained, and at every time I am licensed to a new role, I under oath say that I will be obedient to the disciplines of the church and I will only use the orders and rites of the church that are permitted by law.
"I serve under obedience and you are not going to get me to say anything else."
Elsewhere in the interview she said she hadn't been able to leave the house at any time in the past three months without being recognised.
She said she had even been spotted whilst on holiday in Tenerife: "Without exception that contact has been positive and enthusiastic.
"But there has been a level of contact that feels out of proportion for me as an individual. But I realise it's not about me ... There's just a moment and it happens to be me that's in it. It's not about me as an individual."