He has previously played for various clubs in GCC countries like Ettifaq FC of KSA, Al-Wakrah Sport Club and Al-Gharafa Sports Club of Qatar, Qadsia SC and Kazma Sporting Club of Kuwait and Baniyas SC, Al-Dhafra Club and Ajman Club of UAE. On 1 October 2013, he signed a six-months contract with Dhofar S.C.S.C..
He has been an active member of the senior national team since the early turn of the millennium. Fawzi has been a very key player for the Oman national team, as well as his clubs in play making and scoring. He joined the national team at a very young age of 17 and from the very beginning was a member of the starting line-up. Bashir had held the number 10 shirt since 2001 as well. He was part of the first team squad of the Oman national football team till 2013. Fawzi was selected for the national team for the first time in 2001.
Fawzi has made appearances in the 2003 Gulf Cup of Nations, the 2004 Gulf Cup of Nations, the 2007 Gulf Cup of Nations, the 2009 Gulf Cup of Nations, the 2010 Gulf Cup of Nations and the 2013 Gulf Cup of Nations.
He first showed his talent during the 2003 Gulf Cup of Nations, scoring two goals, one in a 1-1 draw against Yemen and another in a 2-0 win over Qatar. In the tournament, Oman finished at the fourth place, hence reaching its best ever position in the Gulf Cup of Nations competition, reaching the final four round for the first time, with eight points from two wins and two draws.
In the 2007 Gulf Cup of Nations, he scored one goal in a 2-1 win over the hosts the United Arab Emirates in the Group stage. This was the second time when Oman reached to the finals but again they lost to the hosts, the United Arab Emirates. Ismail Matar, the Emirati legend, scored the lone goal of the match as United Arab Emirates won their first ever Gulf Cup of Nations.
Finally in 2009, he helped his team to win their first ever Gulf Cup of Nations trophy. He scored one goal in the 2009 Gulf Cup of Nations in a 2-0 win over Bahrain.
In the 2013 Gulf Cup of Nations, he made two appearances as the captain of the team but failed to score a single goal. Oman again could score only one goal and this time it was from the spot by youngster Hussain Al-Hadhri against Qatar which Oman eventually lost 2-1. Oman failed to qualify for the semi-finals.
Fawzi has made appearances in the 2004 AFC Asian Cup qualification, the 2004 AFC Asian Cup, the 2007 AFC Asian Cup qualification, the 2007 AFC Asian Cup, the 2011 AFC Asian Cup qualification and has also represented the national team in the 2015 AFC Asian Cup qualification.
He scored six goals in the 2004 AFC Asian Cup qualification, a brace in a 7-0 win over Nepal, a hat-trick in a 6-0 win over Nepal and another in a 3-1 win over South Korea hence helping his team to qualify for the 2004 AFC Asian Cup. In the tournament, Oman won four points in a 2-0 win over Thailand and a 2-2 draw against Iran and hence failed to qualify for the quarter-finals.
In the 2007 AFC Asian Cup qualification, he scored a brace in a 5-0 win over Pakistan. Badar Al-Maimani scored one and the only goal of Oman in the 2007 AFC Asian Cup in a 1-1 draw against Australia. In the tournament, Oman won two points in two points in a 1-1 draw against Australia and in a 0-0 draw against Iraq and hence failed to qualify for the quarter-finals.
In the 2011 AFC Asian Cup qualification, he scored one goal in a 2-1 win over Indonesia. Oman failed to qualify for the 2011 AFC Asian Cup.
Fawzi has made thirteen appearances in the 2002 FIFA World Cup qualification, six in the 2006 FIFA World Cup qualification, seven in the 2010 FIFA World Cup qualification and eleven in the 2014 FIFA World Cup qualification.
His only goal for Oman in FIFA World Cup qualification matches came in the First Round of 2010 FIFA World Cup qualification in a 2-0 win over Nepal.
In February 2013, soon after the 2013 Gulf Cup of Nations Bashir announced his retirement from national duty. Basheer and Oman's coach Paul Le Guen were reported to have started drifting apart nearly a year and a half ago when the Frenchman replaced the midfielder with Ali Al Habsi as captain during the World Cup qualifying match against Australia late in 2011. Media reports suggested fresh differences between the two after a friendly against Togo in late 2012 which Oman lost 0-1.Scores and results list Oman's goal tally first.
Omani League (1): 2003-2004; Runner-up 1998–99, 1999–2000
Sultan Qaboos Cup (2): 2000, 2002; Runner-up 1999, 2001
Omani Super Cup (0): Runner-up 2002
Kuwait Crown Prince Cup (1): 2006
Kuwait Emir Cup (1): 2007; Runner-up 2006
Qatar Stars League (1): 2007–2008
Sheikh Jassem Cup (1): 2007
Qatar Crown Prince Cup (0): Runner-up 2007
With Bani Yas
UAE President's Cup (0): Runner-up 2011–12
Etisalat Emirates Cup (1): 2012–13
Gulf Cup of Nations:
Runner-up: 2004, 2007