Criticism earlier this year focused on claims that Bishop's predecessor Carol Fisher's role had been altered, with a new reporting line to Alastair Campbell, the politically appointed director of strategy and comms at Downing Street.
This led to accusations, notably from the Conservative Party, that Campbell now effectively controlled the Government's marketing spend.
Bishop said: 'That was not accurate, she did not have a reporting line to him (Campbell) and I will not either. She was available to offer him advice and that situation hasn't changed. The position is clear - I report to the Cabinet Office.'
He added that there was 'absolutely no truth' in claims that the COI had become a political tool.
Bishop, who quit his role of chairman at Saatchi & Saatchi International earlier this year, is due to take up the role in January.
He said he didn't see Government departments setting up their own PR agency rosters as an issue. But he did add that he was 'looking forward' to talking to officials at the Department for Transport, which last summer took control of the COI's £20m transport ad budget.
The shortlist for the COI CEO post is understood to have included Simon MacDowell, director of communications at the Department of Work and Pensions and Raoul Pinnell, Shell international V-P of global brands and comms.