The accident occurred around midnight Thursday-Friday in Lom Sak district, Phetchabun province while the bus was en route to the northern province of Chiang Rai.
"We suspect the bus driver fell asleep," Major General Sukit Samana, police commander of Phetchabun province, told AFP.
Twenty-eight bodies were found in the ravine and one died in hospital, he said.
Several others were in a critical condition. No foreigners were believed to have been on board.
"The eyewitness who informed the police said the bus went very fast before it plunged into the ravine," Sukit said.
He said more than 100 police, soldiers, civilians and rescue workers had joined the rescue effort.
The bus, which was carrying 40 passengers, was completely destroyed in the accident.
Transport Minister Chadchart Sitthipunt said the bus smashed through the safety barrier of the Phamuang bridge, whose highest pillar stands at 50 metres (164 feet) tall and which links north and northeast Thailand.
"The accident may have been caused by a reckless driver as the bus was travelling at high speed going downhill and it crashed through the bridge railing before plunging into the 50- to 70-metre deep ravine," he said.
The accident occurred as millions of Thais are expected to travel during the New Year period to take advantage of a five-day public holiday starting on Saturday.
Safety standards are generally poor in Thailand and deadly road accidents are common.
At least 20 people were killed in October when a tour bus carrying elderly Buddhist devotees plunged into a ravine in northeast Thailand.
A recent report by the World Health Organization said the country saw some 38.1 road deaths per 100,000 of population, compared to an average of 18.5 in Southeast Asia as a whole.
