The suspected suicide bomber, identified as Naida Asiyalova, 30, of the Russian republic of Dagestan, died on the bus. About 50 people were injured, the Russian news agency RIA Novosti reported.
Police say they are searching for Dmitry Sokolov, 21, Asiylova's husband, who has been missing for more than a year.
"His parents, living in Moscow Region, reported to the police that he had disappeared in summer 2012" after visiting a mosque, Investigative Committee spokesman Vladimir Markin said Wednesday. Sokolov allegedly met Asiyalova three years earlier and shared an interest in "radical Islam," Markin added.
Russia is dealing with a long-running Islamist insurgency centered in Dagestan, where attacks on security forces and police occur regularly, RIA Novosti said.