Bidrose's increase was awarded in March by the council's chief executive appraisal subcommittee - headed by Mayor Dave Cull - but only made public with the release of a previously confidential report yesterday.
Cull said the rise reflected the need to bring Bidrose's pay into line with market value, which had been independently assessed.
He also wanted to reward her "simply outstanding" performance and address a gender pay gap.
Despite that, Bidrose had tried to turn it down, asking instead for a small increase in line with those received by other council staff, Cull said.
The subcommittee rejected that and Cull said he was "adamant" the increase was warranted.
Bidrose was named DCC chief executive in 2013, replacing Paul Orders, and headed an organisation responsible for billions of dollars of ratepayers' assets and 1200 full and part-time staff.
The report released yesterday showed Bidrose began on $350,000 - 85 per cent of the remuneration package offered to Orders, who was himself paid below market value.
The lower pay rate reflected Bidrose's relative inexperience in the role, in line with council policy.
Since then, Bidrose declined a pay rise in her first two years, instead asking for the council to fund half the cost of postgraduate leadership studies at the University of Oxford, while she paid the rest.
After that, Bidrose requested the same austerity imposed on other council staff to be applied to her own increases - taking her total remuneration to $387,000 by late 2018.
That meant she was still paid only 87 per cent of the assessed value of the role, when compared with other local government chief executives.
She was reappointed for a further two-year term in late 2018, and asked for further increases to be linked to those of her staff, but the council's subcommittee disagreed.
Strategic Pay - a New Zealand consultant specialising in remuneration services - assessed the appropriate salary for the role as being between $418,000 and $444,000, while a chief executive showing "added value" should receive between $444,000 and $495,000.
The subcommittee agreed Bidrose "added value" but, given her own requests on pay rates, agreed to award her the lowest end of the range.
The report also warned councillors the increase "will inevitably attract negative media and social media attention", including attempts to "paint councillors in a bad light", which Bidrose "also would prefer not to have".
However, if the council did not adjust her pay, the low rate would create problems when the council had to advertise the role in 2020.
It would either remain too low to attract a good candidate, or any increase needed for a suitable replacement would leave them to face the negative media attention, it said.
