The son of a figure maker Valentin Rainer Bei and his wife Maria Anna, Ambros was born in Vienna on 28th April 1848 and was baptised on the 29th in the Catholic Church of Maria Treu (nowadays better known as the Piarist Church) in that city. On 4th June 1871, Bei, aged 23, was married under the Catholic rite in Vienna to Barbara Cale, aged 21. They had several children. From 1880s until at least the late 1910s, Bei placed advertisements in Viennese newspapers and art journals advertising his sculpture making business. Bei died on 29th October 1926 at 102 Währingerstrasse, Vienna. In 1930, either his own name (included possibly by neglect on the part of the compilers) or that of a son of the same name, and the name of his son Emanuel, who was also a sculptor, were listed in one of the city's directories as showing them living at 22 Währingerstrasse.