Born to Jewish parents in St. Petersburg, Russia, Bolotowsky lived in Baku and Constantinople before immigrating to the United States in 1923, where he settled in New York City. He attended the National Academy of Design. He became associated with a group called "The Ten Whitney Dissenters" or simply "The Ten", a group of artists including Louis Schanker, Adolph Gottlieb, Mark Rothko, Ben-Zion, and Joseph Solman who rebelled against the strictures of the Academy and held independent exhibitions.
Bolotowsky was strongly influenced by Dutch painter Piet Mondrian and the tenets of De Stijl, a movement that advocated the possibility of ideal order in the visual arts. Bolotowsky adopted Mondrian's use of horizontal and vertical geometric pattern and a palette restricted to primary colors and neutrals.
Having turned to geometric abstractions, in 1936 Bolotowsky co-founded American Abstract Artists, a cooperative formed to promote the interests of abstract painters and to increase understanding between themselves and the public.
In the 1960s, he began making three-dimensional forms, usually vertical and straight-sided. Bolotowsky's work was exhibited at the University of New Mexico in 1970.
His work has been exhibited at the Anita Shapolsky Gallery in New York City.