Abraham Bing was born in Frankfurt in 1752, and received his rabbinic training from Nathan Adler. From 1769 to 1778, he served as "Klaus" rabbi (rabbi of a small synagogue) in the town of Offenbach am Main. Between 1778-1796 he served as dayan (rabbinical judge) in Frankfurt, and from 1796 to 1814 he served as rabbi of the town in Heidingsfeld, near Würzburg (Bavaria). In 1813 he was able to overturn previous a 250-year old decree banning Jews from settling in Würzburg proper, and in 1814 he assumed the rabbinate of the city, where he also served as the head of a large yeshiva (rabbinic seminary).
He was an opponent of the Reform movement. Several of his pupils played a major role in nineteenth century Orthodoxy in Germany:
Rabbi Abraham Bing died in Würzberg in 1841, having resigned from the rabbinate two years earlier. Of his writings, only Zichron Avraham (Remembrance of Abraham) was printed (posthumously, edited by Bamberger).