The source said the driver, in his 50s, tried to prevent a man who was not wearing a face mask from boarding the bus with his dog.
The driver also asked four other passengers, who had already boarded the maskless bus, to get out.
Face masks are mandatory in public transport in France, where the Covid-19 epidemic claimed the lives of nearly 30,000 people.
The driver was repeatedly struck in an assault that resulted in serious head injuries, the source said.
He was unconscious when he arrived at the hospital and doctors declared him brain dead Monday.
A man in his thirties was arrested on Sunday and four others were arrested on Monday, the prosecution said.
Regional bus services were cut on Monday after several of the driver’s colleagues refused to work to protest the brutal attack.
The mayor of Bayonne, Jean-René Etchegaray, addressed employees of the bus company on Monday.
“We have witnessed a particularly violent and barbaric act,” he said, calling for the perpetrators to be brought to justice and for a penalty “severe enough” to serve as a warning to others.