The bus was trying to overtake a lorry when it collided head-on with another vehicle and went over the cliff, injuring 24 passengers.
High speed could have contributed to the crash on Sunday night local time.
Accidents on Bolivia's poorly maintained roads result in hundreds of deaths every year.
The bus, which was operated by a company called Totai, was travelling from the country's administrative capital, La Paz, to the Amazon town of Rurrenabaque.
The accident happened near the municipality of Coroico in a mountainous region.
There are at least two children among the victims, highway patrol chief Fernando Rojas said. Some of the injured are
reportedly in a critical condition in hospital.
Mr Rojas told El Diario newspaper (in Spanish), that the driver, who was injured in the crash, had been reckless and ignored the signs in the narrow road.
Rescuers used a rope to climb down the cliff and brought up the victims and survivors one by one, AFP news agency reported.
Writing on Twitter, President Evo Morales urged bus drivers to take more care, saying he was "very sad about the terrible accident".
Some 1,000 people die and 40,000 are injured in accidents on Bolivia's roads every year, according to official data quoted by Efe news agency.
In January, 22 people died when two buses collided near the western city of Oruro. In February, a bus and a lorry crashed, also near Oruro, killing 24 people.