Busch was born on July 10, 1839, to Ulrich Busch and Barbara Pfeiffer in Kastel, then a district of Mainz in the Grand Duchy of Hesse. He was the twenty-first of twenty-two children. His wealthy family ran a wholesale business of winery and brewery supplies. Busch and his brothers all received quality educations, and he graduated from the Collegiate Institute of Belgium in Brussels.
In 1857, at the age of 18, Busch emigrated with three of his older brothers to St. Louis, Missouri which was a major destination for German immigrants in the nineteenth century. Because he had so many siblings, Adolphus did not expect to inherit much of his father's estate and had to make his own way. Since St. Louis was home to so many German immigrants, the market for beer was large. The city also had two natural resources essential for manufacturing and storing beer in that time, before refrigeration: the river provided an ample water supply; and the city had many caves that would keep beer cool.
His brother Johann established a brewery in Washington, Missouri. Ulrich Jr. married a daughter of Eberhard Anheuser in St. Louis, and settled in Chicago. Anton was a hops dealer who later returned to Mainz.