The attack in the Volga River city of Volgograd, which also injured more than 30 people, was the deadliest outside the volatile North Caucasus in the past three years.
An official at the Investigative Committee -- Russia's equivalent to the US Federal Bureau of Investigations -- said the suspected bomber was the wife of a North Caucasus rebel commander.
Footage broadcast on state television showed a green and white city bus standing mangled in the middle of the street, its windows blown out on the left side.
The Investigative Committee said officials had opened a formal probe into terrorism, murder and the illegal use of firearms.
"According to preliminary information, a native of Dagestan, 30-year-old Naida Asiyalova, blew herself up," investigators said in a statement, referring to one of the North Caucasus' most violent regions.
"She boarded the bus at one of the bus stops and an explosion took place almost immediately afterwards."
An official at the Investigative Committee said the suspected bomber was the wife of a rebel commander.
Investigators said 33 people, including a small child, had been injured. Twenty-eight victims were sent to hospital, eight of them in "extremely grave condition"
Officials said the packed bus was carrying about 40 passengers at the time of the explosion.
"There were lots of students on the bus," a man named Vladimir, whose daughter survived the explosion, told Moscow Echo radio from Volgograd.
"It was a powerful explosion -- a huge blast," he said.
"The bus was torn to pieces. When I came to pick up (my daughter), half the bus was simply not there."
Security remains a concern throughout southern Russia ahead of the February 7-23 Winter Games in the Black Sea resort of Sochi, which is located next to the North Caucasus.
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