Barend Jacobus Erasmus was born to Barend Jacobus Gerrit Wessel Erasmus and Susara Catharina Elizabeth Horak on 29 December 1918 in Johannesburg. His father was a businessman and farmer who also owned a butchery in Parys.
Schooled in Zeerust, he showed leadership qualities by captaining the school rugby team. During the Great Depression of the 1930's he was forced to leave school and seek employment. In June 1936 Erasmus was employed by the Johannesburg Municipal Transport Service to scrub trams and buses. He was elevated to the position of conductor and later got involved in the Johannesburg Municipal Transport Workers Union (JMTWU). Erasmus was influenced by the President of the JMTWU, Johannes Jacobus (Jan) Venter.
On 23 June 1943 he was elected to the executive of the union. Three years later he was promoted to the position of senior trustee. In 1949, after Venter was elected General Secretary, Erasmus became President. He held the Presidency until 1969 when he became the organiser for the JMTWU. Erasmus took over Venter's position when he died in 1953, and held the position for 20 years. Members of the JMWU gained immensely from Erasmus's leadership. He won longer sick leave privileges for workers at Arbitration Court, in 1956 he negotiated a 40 percent consolidation of cost of living allowance for all municipal employees, which was increased to 100 percent in 1961.
Erasmus was a member of South African Council of Transport Workers (SACTW) from 1948. He served the union as the Treasurer for four years, Vice President for five years. In 1960 he was elected President in 1960. He was elected to the national executive committee of the South African Trades and Labour Council from 1949. He was a member of the Unity Committee that led to the formation of the Trade Union Council of South Africa (TUCSA). When TUCSA was formed in Durban in October 1954 he became national executive committee member. In 1967 Erasmus was part of the delegation from TUCSA to meet with the Minister of Labour, Marais Viljoen to convince him to recognise Black trade unions.
Erasmus was also passionate about sport; rugby in particular. He was a founder member of the Johannesburg Municipal Sports Club and later became Vice-President of its gymnastics section. From 1945 he was actively involved in the Transvaal Rugby Football Union.
At the time of his death in 1973 he was still an executive member of SACTW and the Special Tribunal dealing with disciplinary measures at Johannesburg Municipal Sports Club.
Erasmus was married to Magdalena Pelser and they had two sons and one daughter. In 1964 he divorced Pelser and married Cynthia Francis Snyman in 1967. Their marriage was blessed with one daughter.