Born in Narrandera, New South Wales, Bashir graduated from the University of Sydney in 1956 and held various medical positions, with a particular emphasis in psychiatry.

However, wanting to assist people suffering from mental illnesses, Bashir eventually decided to take up postgraduate studies in Psychiatry.

To make this easier, in 1968 Bashir and her family moved back into central Sydney to Mosman on the North Shore, purchasing a Middle Harbour-waterfront house at 7 Shellbank Avenue for $57,000 from yachtsman Gordon Reynolds.

On 13 June 1988 she was made an Officer of the Order of Australia (AO) "In recognition of service to medicine, particularly in the field of adolescent mental health".

[16] Upon her appointment, Sydney Morning Herald journalist David Marr noted, "what could be more valuable behind the scenes in Macquarie St than this woman's unique expertise with troubled adolescents?

On the very day of her inauguration, Bashir agreed to become Patron of the Gay and Lesbian Counselling Service, which addresses mental and social issues in the LGBT community.

In 2005 Bashir opened the Sydney Gay and Lesbian Mardi Gras Festival in a concert in Hyde Park and credited the event with fostering "that sense of freedom which springs from the considerable diversity within our society – diversity of race, religion, culture and also sexual orientation [...] We must never take these things for granted because most of you would agree that across the world today an extraordinary winding back to many previously discarded attitudes is taking place, not only affecting gay and lesbian groups, but women's health and many aspects of social justice".

[20] In 2002, Bashir became Patron of the Australia-Vietnam Medical Trust and became intimately involved in collaborative health programs in Vietnam, particularly in rural areas.

[21] On 17 May 2001, the Governor-General, Sir William Deane, invested Bashir as a Dame of Grace of the Most Venerable Order of the Hospital of St John of Jerusalem (DStJ).

[29] Bashir was involved in the high-profile legal case against a psychiatrist called Dr Brendan O' Sullivan and the NSW health service, in which she was falsely cited in his dismissal; using the opportunity to claim sovereign immunity, usually only used by the Crown.

[31] It was announced on 15 October 2007 that the Queen, on the recommendation of Premier Morris Iemma, had extended Bashir's appointment as governor for a further four years to February 2012.

[37][38] On 14 September 2011, Liberal Premier Barry O'Farrell announced that he had recommended to the Queen that Bashir's term be extended for another two years to 2014, which had been accepted: "Over the past 10 years the Governor's caring nature, her genuine interest in local communities and her extraordinary work rate have endeared her to people everywhere...Because of her diverse background, career and interests, Professor Bashir has given a historic and important post a contemporary relevance and resonance.

"[39] From the time of her commencement as governor, Bashir, like her immediate predecessor, did not reside in Government House, Sydney, retaining it for reception and official purposes.

[40] On 19 April 2012, Bashir was presented with the insignia of a Grand Cordon of the National Order of the Cedar by the President of Lebanon, General Michel Suleiman, at Government House, Sydney, during his state visit to Australia.

[49] In the 2014 Queen's Birthday Honours, Bashir was made a Dame of the Order of Australia "For extraordinary and pre-eminent achievement and merit in service to the administration, public life, and people of New South Wales, to medicine, particularly as an advocate for improved mental health outcomes for the young, marginalised and disadvantaged, to international relations, through the promotion of collaborative health programs, and as a leader in tertiary education".

[50] In September 2014, her official portrait as governor by Archibald Prize finalist Mathew Lynn was unveiled at Government House by Premier Mike Baird.

[51] Ahead of her impending retirement from office on 1 October, Bashir noted that the time was right for her to go just short of the record in office set by Sir Roden Cutler: "a war hero who lost a leg serving this country, I would like to think of him as the longest serving governor"[52] and that "The time is right, It was myself who said I would conclude my term around the anniversary of World War One.

[53] She made clear at the time of her retirement her interest in continuing her community work, particularly through the area of post-traumatic stress disorder in Australian Defence Force veterans.