"There is reason to believe that the explosive was planted either underneath or on the floor of the bus," a police source was quoted as saying.
Security at the scene was tight and some photographers were either detained or had their equipment confiscated by the authorities.
Togliatti lies more than 1,000km to the southwest of the capital Moscow and is home to the AvtoVaz, Russia's largest manufacturer of autmobiles.
Organised crime groups, many of them involved in trading car parts, fight regular battles for control of illegal business opportunities.
Explosive devices without shrapnel, like the one Russian media said may have caused the bus explosion, are often used by criminal gangs against each other.
Al Jazeera's correspondent Jonah Hull, reporting from Moscow, said the blast location is far from the North Caucasuses and does not offer an obvious Chechnya connection.
"The focus is very much on conventional terrorism," he said.
"There had been fears that groups keen on destabilising the election process might choose this time to do it. Investigators will be looking closely at whether those fears are coming to fruition."