The unpopular Abbott survived a confidence vote on his leadership on Monday initiated by MPs from his conservative Liberal Party which was sparked by poor poll ratings, policy backflips and his perceived high-handed decision-making.
Foreign Minister Bishop, seen as a potential future leadership contender along with Communications Minister Malcolm Turnbull, said she supported him but he must listen more to the concerns of his colleagues.
Backbench frustration has focused on how Abbott's office is run by his powerful chief-of-staff Peta Credlin, with one MP describing it as a climate of "fear and intimidation".
Calls are growing for Credlin to be sacked so the party can move forward."I think people have been very frank and blunt in their assessment of the performance of the prime minister's office," said Bishop.
"And the prime minister is a smart man, he will take those issues into account," she told the Australian Broadcasting Corporation.
Bishop added that Abbott "has shown a great deal of humility in accepting that he made some wrong calls".
"And he has put in place a number of changes to the way he does things, the way his office does things and the way cabinet consults with the backbench in the party room more generally."
Treasurer Joe Hockey's harsh first budget last year and his inability to properly explain health, education and welfare cuts to the electorate has seen calls for his head to also roll.
But Abbott backed him on Monday and Bishop did the same, saying: "Joe's heard the messages from the backbench".
Abbott, who survived the "spill" motion 61 to 39, faced a party room meeting Tuesday morning to explain his new approach.
Former assistant treasurer Arthur Sinodinos -- who backed Abbott's removal -- said the meeting would be a "new paradigm" for the government.
"I suspect you'll find a lot of MPs on their feet raising issues," he said.
After surviving the move to unseat him, Abbott urged an end to disunity and vowed to be more consultative.
"I accept that things have got to be a little different in the future -- quite considerably different," he told national television on Monday evening.
Since being elected in September 2013, the government has sealed free trade deals with China, South Korea and Japan. It also killed off controversial carbon and mining taxes and sharply reduced the number of asylum-seeker boats arriving in Australia.
But proposed savings to curb a ballooning budget deficit alienated many voters, as did Abbott's awarding of a knighthood to Britain's Prince Philip.
