He was born on 20 November 1882 in Warsaw to a gentry family of an insurance official Jan Bobiński and his wife Stanislava (Polish Stanisława Tołwińskich).
He was one of the directors of the Polish-language Trybuna newspaper published in revolutionary Moscow and a notable promoter of the communist movement among the Polish expatriates in Russia.
A representative of the SDKPiL at the Brest peace talks, on 7 February (25 January) 1918 he announced the "Declaration of the representatives of the working people of Poland", calling for "the elimination of police barriers between the three parts of one country" and "the immediate withdrawal of the occupying troops and the cleansing of Poland from all government bodies established by occupation authorities".
During the Soviet offensive on Warsaw during the Polish–Soviet War, Bobiński became the secretary of propaganda in a shadow government formed by the Communist Party of Poland (the Provisional Polish Revolutionary Committee), headed by Julian Marchlewski and Felix Dzerzhinsky.
In 1922–1924, he became a professor of philosophy and rector of the Gorky Ural University in Yekaterinburg, and beginning in 1925 was a member of the Polish Bureau (Polburo) in the Central Committee of the All-Union Communist Party of Bolsheviks.
He was arrested in the evening of 15 June 1937 by the NKVD during the Great Purge on charges of participating in the counter-revolutionary organization Polish Military Organisation ("POW"), conducting espionage activities in the USSR on behalf of Polish intelligence, having knowledge of other members' terrorist plans, and Luxemburgism.