Mr Bradshaw, a former BBC journalist, has clashed with the BBC since becoming Culture Secretary in June.
He supports plans to use part of the TV licence fee to fund regional ITV news, a move known as "top-slicing", which BBC management is opposed to.
When Sir Michael was asked about the relationship between the BBC and the government, he said: "The BBC would always want to co-operate with the government of the day.
"And as far as I'm concerned we continue to do that, but we start from the position of not feeling that we've got to keep ministers happy."
He also suggested that the government had taken issue with the trust because it had the "temerity to go to the public, to ask their views about some government proposals and we've come up with answers which the ministers don't like".
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.