The most prominent exponent of German Romantic flute-playing in the first half of the 19th century, A.B. Fürstenau was the son and flute pupil of Caspar Fürstenau (1772–1819) and the father and teacher of Moritz Fürstenau (1824–89). After an early career as a traveling virtuoso alongside his father, he was appointed principal flutist of the Dresden orchestra by Carl Maria von Weber in 1820.

All his life Fürstenau continued to play the traditional German keyed flute, preferring instruments by Wilhelm Liebel and others, though he allowed his son Moritz to study the ring-key flute with Theobald Boehm. However on succeeding his father in Dresden in 1852 the son had to give up the new flute and return to the older model, which was preferred for its ability to blend with the other woodwinds and its soulful ability to produce a large palette of tone colors (Modulationsfähigkeit).

A.B. Fürstenau wrote articles about flute playing in 1825 and 1838 that tell us much about the special style and feeling of the time. He also gave extensive technical directions, especially for the fingering of the German and Viennese-type keyed flute, in his flute tutors of 1826 and ca. 1844.