The complaints committee also recommended that council chief executive Richard Briggs arrange a workshop for elected members to attend covering topics relating to the Code of Behaviour.
After the meeting Councillor Bunting released a statement saying he he was sorry.
"I misjudged how offensive it would be to her and as a result how hurtful it could be to women, Christians and the general public. I misjudged badly and apologise unreservedly," Mr Bunting said.
"I will continue to serve the Hamilton community with honesty and am extremely motivated to win back the trust of those I have offended.
"I am sorry."
Mrs Cuming told Hamilton News she was pleased that the situation was dealt with promptly by mayor Andrew King.
"While it was never my intention to see Cr Bunting punished for what he did it is pleasing to see Hamilton City Council take the very real issue of sexist and harmful behaviour towards women seriously," Mrs Cuming said.
"While I am still puzzled and will be puzzled forever more why Cr Bunting, or anyone for that matter, would find a crude reference to Jesus and a particular sexual act funny or that I would get a laugh from it, I nonetheless accept Cr Bunting's apology."
"It would have been nice if he had found it within himself to apologise to me in person, but only he knows why he could not extend me that courtesy."
The committee was made up of mayor Andrew King and councillors Siggi Henry and Leo Tooman.
They reviewed screen shots of the conversation between Mr Bunting and Mrs Cuming while also reviewing the video that Mr Bunting had sent to her.
Mr Bunting told the committee he was messaging the recipient in a personal capacity.
The committee accepted that Mr Bunting did not make the video. The committee also accepted that Cr Bunting did not send the still image posted on the recipient's social media account.
The committee said the video contained material of a sexual nature which was inappropriate and offensive while also finding the video religiously offensive.
Following decision involving Mr Bunting, the complaints committee met to consider a complaint about comments made by councillor Garry Mallett on Radio New Zealand's Checkpoint programme.
The complaint related to the phrase 'limp-wristed.'
The committee said that in the context in which it was made it did not breach the council's Code of Conduct Policy.
Mr Mallett was directed to attend and complete the council's workshop on Code of Behaviour.
