Henriëtte Hilda Bosmans was born into a very musical family. Her father, Henri Bosmans (1856-1896), was the solo cellist of the Concertgebouw Orchestra of Amsterdam; he died before Henriëtte's first birthday.
Her mother, Sara Benedicts (1861-1949), was a piano teacher at the Amsterdam Conservatory for over forty years. Henriette (Jetty) took piano lessons from her mother and at seventeen was awarded her diploma cum laude from the Society for the Advancement of Music.

Early on, Henriette began performing regularly as a soloist at the Amsterdam Concertgebouw under the baton of such conductors as Willem Mengelberg, Ernest Ansermet and Pierre Monteux.
She showed little interest in teaching. When, in 1943, Willem Pijper invited her to teach at the Rotterdam Conservatory, she declined.
A free spirit with no desire to tie herself to scheduled lessons, she carefully guarded her independence.

Together with the violinist Francis Koene, Henriette gave the Dutch premiere of Alban Berg's Kammerkonzert für Klavier und Geige mit dreizehn Bläsern. In 1934 she and Koene announced their engagement and Bosmans composed the Concert Piece for Violin and Orchestra as a gift to her fiancé. Koene fell ill, however, suffering from a brain tumor, and died the following year, never having performed the work. Overcome with grief, Henriette composed very little until the end of World War II. Being half-Jewish, she was barred from giving public performances from 1942, though she did often perform in private.