A government spokesman said the toll was expected to rise as some of the injured had received multiple burn and splinter wounds in the blast.
The bus was carrying 50 people when the bomb exploded at Mazgaon village, 410km from the state capital Guwahati.
The vehicle was quickly engulfed in flames, according to passengers.
A police official said the outlawed United Liberation Front of Assam (ULFA) rebel group was suspected to have carried out the attack.
The blast is the fourth in Assam in the past two weeks and security officials see the escalation in violence as an attempt by ULFA to show it still remains a powerful force.
The rebel group, which has bases in Bhutan, suffered heavy reverses when the Himalayan kingdom launched an army offensive last year in an attempt to eliminate them from the neighbouring country.
"The serial blasts are acts of desperation with the ULFA trying to make its presence felt," said Assam chief minister Tarun Gogoi.
More than 10,000 people have lost their lives to insurgency in Assam in the past two decades.