Before he surfaced in a Montreal courtroom in April, few people in the small world of bike-sharing had heard of the New Yorker with access to deep pockets.

Jonathan Schulhof, 40 years old, wanted to buy out of bankruptcy a major supplier of shared bicycles and docking stations where riders park them for systems such as New York's Citi Bike. He told the court of his ambition, according to the Montreal Gazette, to "proliferate bike-sharing around the world."

While Mr. Schulhof lost his bid for the supplier to a globe-trotting Canadian businessman, he is now poised to become a major player in a fledgling industry behind bike-shares popping up in cities across the U.S.

Mr. Schulhof heads a new investment firm, REQX Ventures, which is close to a deal to purchase a controlling stake in Citi Bike's operator, according to people familiar with the matter. The operator, Alta Bicycle Share Inc. of Portland, Ore., has similar programs in places such as Boston, Columbus, Ohio, and San Francisco. Outside the U.S., Alta runs programs in Toronto and Melbourne.

Much about Mr. Schulhof and his plans for bike-sharing remain a mystery. A Stanford-trained lawyer who studied French literature and government at Dartmouth College, Mr. Schulhof has spent much of his career inside corporate boardrooms and at private-equity firms.