She studied painting in Lviv and at the Academy of Fine Arts in Kraków, in the studio of Wojciech Weiss (although we read in J.W. Sienkiewicz's 'Anders Artists' that this fact is confirmed by Stanisław Frenkiel, but this is not confirmed by the list of the artist's students in the study 'Wojciech Weiss at the Academy of Fine Arts in Kraków'). Deported to the Soviets during the war, she escaped with the Anders Army to the Middle East in 1942. She became involved in the work of the Polish Art Studio, founded in Tehran by Roman Schneider. In the Painting Studio, together with Maria Schneider and Alicja Drwęska, Zofia Bobrowska executed, on commissions from Polish institutions established in Iran, oil portraits of members of the Polish government and army commanders and specialised in painting still lifes. In Tehran, at the end of 1943, Bobrowska took part in a show of the artistic output of 26 Polish artists-soldiers, organised in the building of the Iranian Theatre. In January 1944, the artist took part in an exhibition in Beirut, grouping works by artists-soldiers and painters not associated with the 2nd Corps.

The artist took part in the classes of the Polish School of Painting and Drawing, directed by Bolesław Baake, but she was not associated with the school, as she most likely continued to work with Maria Schneider, also arrived in Beirut. After a year in England, the artist emigrated to Canada in 1949 and settled in Montreal. She tried to earn a living by painting commissioned portraits and views of Montreal. Her painting Old Montreal Houses was purchased for the private collection of Sir Huntley Drummond. In 1950, the artist showed paintings pressed in metal at the Canadian National Exhibition and in the same year she participated in the Exhibition of Polish Artists in Exile Residing in Canada at the Montreal Museum of Fine Arts. In 1951 she participated in the Exhibition of Slavonic Art at Montreal University and in 1954 in the Polish Art Exhibition at McGill University.

The artist was a member of the Polish Decorative Club founded in Montreal in 1955. At the CNE, in 1956, the Polish Decorative Club organised a booth featuring Polish arts and crafts. In 1958, Bobrowska moved to Ottawa, where she continued her artistic work seeking new forms of expression in metal. At the Exhibition of Arts and Crafts of Polish Canadians at the National Museum in Ottawa, in 1962, the artist showed a painting, 'Madonna', extruded in aluminium, modelled on a painting of the Madonna of Częstochowa. The artist spent summer periods on Prince Edward Island finding plein air painting opportunities there. Feeling connected to Montreal's artistic community, she twice supported the Polish Library by donating her paintings for auction.

An exhibition in Ottawa in 1962 was her last recorded artistic presence. No photographic documentation has survived, apart from three poor-quality reproductions in A. Wołodkowicz's study "Polish Contribution to Arts and Sciences in Canada".