Qureshi was born to Ghulam Murtaza Qureshi, on 10 August 1959 at Motan Pur Mohalla in Ratodero, Larkana District in Sindh.
He started his political career as a student worker of the Jeay Sindh Students Federation (JSSF) during his masters studies at the Agriculture University, Tando Jam (Sindh). As a student, he also played democratic role by participating in the movement of restoration of democracy MRD during General Ziaul Haq’s tenure.
After the death of leader GM Syed (who was his political mentor), the party decided to elect Qureshi as the new chairman of JSQM.
He took part into students' politics. He joined in Jeay Sindh Students Federation in the year 1976. He was elected as President of the Federation; Tando Jam Unit in the year 1980 but after two years (1982) was elected as Central Vice President of the Federation. He was also elected as Central President of the Federation in the year 1986. In 1990, he was re-elected for the same post. Nevertheless, in the year 1995, Jeay Sindh Quami Mahaz was formed when he was behind the bar but was elected as Deputy Convener. He was also elected as Secretary General of the Mahaz in 1996 and finally elected as Chairman in the year 1998. Mr Bashir played a role in mobilizing the members of the Federation and worked hard to strengthen the Federation.
Finally, he was set free in August, 1986. Mr Bashir was again arrested on August 11, 1988 after Sindhi-Mohajar riots. This time, he was jailed for 18 months. Again, he was arrested on Jan 02, 1994 (PPP regime) for two years. Later he was arrested on Jan 17, 1999 on his way to attend the birth celebration of Saeen G. M. Syed and was set free in November 1999 after a struggle of 11 months. Mr Bashir has remained in prison for the total period of 6 years and 10 months. He is author of his book entitled "Jaagya Junge Jawaan" in Sindhi language, published in 1989 which is collection of various speeches delivered by him. Mr Bashir was awarded "G. M. Syed National Award" in the year 1997. He was arrested on September 15, 2011 by rangers and was charged for carrying weapons, he was released by court as the arms were duly licensed. His arrest provoked automatic protest and complete strike throughout Sindh was observed.
Qureshi contributed to resolve the tribal feuds among different Sindhi tribes, and set the tradition of taking delegations to the rival groups to convince and encourage them to resolve their bloody feuds through traditional dispute resolution mechanisms, through the involvement of the notables.
Qureshi died mysteriously at the age of 54 on April 7, 2012 at Sakrand (Sindh). Qureshi was visiting the JSQM supporters in Dera Magsi village, Nawabshah District, when he suddenly lost consciousness after having a dinner with other party co-workers. He complained of chest pain followed by a cough. Qureshi was shifted to a local hospital, where he breathed his last at around 2:45am.
On 19 April 2012, a forensic medicine and pathology team from government medical institutions of Sindh reported that Bashir Qureshi reason of death may be high phosphorus or cardiac arrest, but were unable to confirm it. Party activist claimed he was poisoned, but his family did not want investigation and refused to help investigation committee
Qureshi left behind his widow, three sons and four daughters. His eldest son Sunan Qureshi is the current chairperson of the party (JSQM).