Anna Bilińska was born into the family of a doctor and she spent a part of her childhood in Vyatka, Ukraine, where she was given her first drawing lessons by Michał Elwiro Andriolli. After she and her parents moved to Warsaw, she started attending music school. Eventually, in 1878, she joined the School of Drawing directed by Wojciech Gerson, who acknowledged her great talent. Maria Gażycz, Aniela Wisłocka and Zofia Stankiewiczówna, also students of Gerson, became her friends. In 1882, Bilińska traveled abroad. She visited Vienna, Munich, Salzburg, Padua and Venice. In November 1882, she began studies at Academie Julian in Paris in a class for women. Rodolphe Julian, who acknowledged her great talent, allowed her to continue her education in his school without charging tuition. This was significant because the artist's father died in 1884 leaving her penniless. One year later, Wojciech Grabowski, her fiancee, a drawer and a painter, also died. In despair, after a deep nervous breakdown, and in order to regain her health the artist traveled to Normandy and Bretagne, staying at the seaside in La Rochelle, the island of Oleron, Bedonet and Beg-Meil. There she produced many sketches and paintings, mostly landscapes. Returning to Paris in 1886, Bilińska rented a studio and was appointed head of an academic studio by Julian, a position she retained until 1892. In 1890, she made a short trip to Berlin, where an American, Corning Clark, commissioned her to paint the pianist Józef Hofman.
In 1892, she married a doctor of medicine, Antoni Bohdanowicz, and returned to Warsaw where she intended to set up a school of painting for women, an idea she had been considering for some time. In an 1883 letter to Wojciech Grabowski, she wrote: "I want to set up a school for women in Warsaw. [...] My school will be based on a Parisian model, but the program will be broader, as additional instruction will be included in it." Her plans were never realized because the artist died suddenly due to an attack of rheumatism that exacerbated her underlying cardiac disease.
Anna Bilińska earned a living selling her works. Her paintings were purchased mostly in France and Great Britain, where they were very popular. As her oeuvre is scattered among many collections, it is hardly known. She created portraits (in crayon as well as oils) characterized by her skillful realistic technique that enabled her to grasp perfectly the sitter's likeness. The artist used a limited selection of hues, and the refinement of her colors is most clearly visible in her pastels. Her style: "follows the canon of aesthetic realism, in which skill and simplicity are combined with well planned composition, faultless drawing, the ability to shape figures, color harmony and a refined finish" (see Tyczyńska 1995, p.139).
Her genre scenes are rather obscure – A Polish Peasant, Mother with a Child. A separate position in her oeuvre is taken by landscapes – A Sunset, Cliffs, A Coast, The Sea in the Rain – which have been shown frequently, They are referred to as "pochades" (sketches) in which Bilińska turned to Impressionism, though she criticized that contemporaneous style in the above-quoted letter to Wojciech Grabowski (after having seen an exhibition of Monet's works in 1884). Her husband confided that she was captured by transitory impressions: "She was struck, during a stroll, by some kind of mood. She grasped the paintbrush, and instantly, before her vision faded, she transferred it onto the canvas, marking only the main, central or lateral views in a hurry. The rest was held in her memory to be finished later. This often lasted 10-15 minutes and in reality it was already entirely different" (see Bilińska 1928, p. 137).
Her works were shown regularly at TZSP (The Society for Encouragement of the Fine Arts in Warsaw, (1876-1888, 1891-1899, 1901, 1903, 1907) and at the Society of Friends of the Fine Arts in Kraków (1883, 1885-1886, 1891, 1893-1895). Her debut in Paris took place in 1884 at the Salon, where her drawing Figure of a Woman was displayed. She then contributed regularly to group exhibitions, including the Paris Salons (1885, 1887, 1892). She was awarded a silver medal for her Self-portrait (currently at the National Museum in Kraków) at the Universal Exposition in Paris in 1887, thus achieving spectacular international success. Her work was greatly appreciated in London as well when it was exhibited at the Royal Academy of Art (1889) and the Grosvenor Gallery. In 1891, seven works by Bilińska were shown at the Universal Exposition in Berlin, where the artist received a gold medal.