Bartum joined the British Museum's Department of Prints and Drawings in 1979. She became Curator of German prints and drawings in 1991. In the latter role she was also responsible for coordinating between departments, research into the provenance history of items held in the British Museum collections which may relate to the Nazi era.
Bartrum's first book was German renaissance prints 1490-1550, which was the catalogue of an exhibition held at the museum during 1995.
She is an authority on the art of Albrecht Dürer and her catalogue for the 2002-03 exhibition Albrecht Dürer and his Legacy, published jointly by the British Museum Press and Princeton University Press in 2002, won the 2003 Art Newspaper/AXA Exhibition Catalogue of the Year Prize. She edited a work on Edward Munch's prints in to accompany a 2019 exhibition Edvard Munch: love and angst, published by Thames & Hudson in collaboration with the British Museum.
Bartrum retired from the British Museum in November 2019.