Albertus Bernhardus Bartmann matriculated in 1883 through the University of the Cape of Good Hope and three years later was awarded the degree Bachelor of Arts (BA) by the same institution. He continued his studies at Victoria College, Stellenbosch, and in 1888 he (and W.C. Meredith) were awarded the degree Master of Arts (MA) in Mathematics and Natural Philosophy by the university, having passed its written examinations in the following papers: geometry, algebra and trigonometry; conics; differential and integral calculus; statics and hydrostatics; dynamics and hydrostatics; geometry of three dimensions; and geometrical optics. They were only the second and third recipients of this particular degree, following H.J.L. du Toit* in 1878, though an MA degree in Natural Science had also been awarded to C.F. Juritz* in 1886.
In June 1888 Bartmann was appointed assistant teacher at the public school in Stellenbosch, and a year later promoted to principal of the public school at Richmond. In April 1892 he became a deputy-inspector of schools in the Eastern Cape and then inspector of schools at Caledon, Western Cape, a post he held until 1896. He then moved to Pretoria, in the South African Republic (Transvaal), where he was appointed lecturer in mathematics at the Staatsgymnasium (government high school) in July 1897. That same year he applied for naturalisation as a citizen of the republic. There he remained until the outbreak of the Anglo-Boer War (1899-1902), when he resigned both his post and as a member of the Board of Examiners of the republic.
After the war Bartmann became Superintendent of Education of the Orange River Colony (now the Free State). In January 1906 he was appointed to a second chair in mathematics (the first being occupied by Prof. A.H. MacKenzie*) at Victoria College (from 1918 the University of Stellenbosch). He remained there until June 1921. In 1909 he was an examiner in mathematics for the second mining examination of the University of the Cape of Good Hope.