Alfred Arthur Bodkin studied mathematics at King's College, Cambridge, obtaining the degrees Bachelor of Arts (BA) in 1869 and Master of Arts (MA) in 1874. He was assistant master at Haileybury College, near Amwell, Hertfortshire, from 1874 to 1878, and then worked as a tutor in Toronto, Canada. From 1881 to 1902 he was vice-principal and lecturer/professor of mathematics at the Diocesam College ("Bishops") in Rondebosch, Cape Town. At this time Bishops was a private school that also presented some courses at university level. In addition to mathematics Bodkin taught natural science from 1884 to 1886. He was admitted to the MA degree of the University of the Cape of Good Hope in 1881, on the basis of his British qualifications. In 1883 he became a member of the South African Philosophical Society and remained a member for some 20 years.
Bodkin collected plants for Harry Bolus* in various parts of the Cape Colony and sometimes accompanied the latter on collecting trips. For example, in 1897 the two of them and the Colonial Botanist, Peter MacOwan*, made a botanical trip to Clanwilliam and Wuppertal during which many specimens were collected. Bodkin was mentioned as an important collector by Rudolph Marloth* in an 1895 review of science in South Africa. His specimens were passed on to Bolus and ended up in the Bolus Herbarium and South African Museum Herbarium in Cape Town. Two books of watercolour paintings of his plants were prepared by his wife, Ada M. Shaw.
Bodkin was a member of the council of the University of the Cape of Good Hope from 1889 to 1902. In the latter year he returned to England and settled in Oxford where he was a church organist. He is commemorated in the species names Disa bodkinii, Erica bodkinii, Nemesia bodkinii, Agathosma bodkinii, and Pachites bodkinii, several of which were named by Bolus.