The bus carrying six teachers and 39 students in elementary and junior high school was on a highway north of the capital when the fire started and spread so quickly many were unable to escape.
Trairong Phiwpan, head of the police forensic department, said 23 bodies were recovered from the bus.
The recovery work and confirmation of the total dead had been delayed earlier because the burned vehicle, which was fuelled with natural gas, remained too hot to enter for hours.
The families were driven to Bangkok on Wednesday to provide their DNA samples for the identification process.
The driver, identified by the police as Saman Chanput, surrendered on Tuesday evening several hours after the fire.
Police said they have charged him with reckless driving causing deaths and injuries, failing to stop to help others and failing to report the accident.
The driver told investigators he was driving normally until the bus lost balance at its front left tyre, hit another car and scraped a concrete highway barrier, causing the sparks that ignited the blaze, Chayanont Meesati, deputy regional police chief, told reporters.
The driver said he ran to grab a fire extinguisher from another bus that was travelling for the same trip but he could not put out the fire, and ran away because he panicked, Chayanont said.
Police said they are also investigating whether the bus company followed all safety standards.
In an interview with public broadcaster Thai PBS, bus company owner Songwit Chinnaboot said the bus was inspected for safety twice a year as required and that the gas cylinders had passed the safety standards. He also said he would compensate the victims' families as best as he could.
Three students are hospitalised, and the hospital said two of them were in serious condition. A seven-year-old girl suffered burns on her face, and a surgeon said doctors were doing their best to try to save her eyesight.
