The accident happened in front of Soi Lard Prao 125 near the Bang Kapi Market, Pol Capt Thanathorn Yodkaew, deputy inspector of Lard Prao police station, said.
The victim was identified only as Benjawan, 33, an employee of an eyeglasses shop nearby.
Police arrested the bus driver, Somjit Momphan, 64. He was charged with reckless driving, causing death.
Somjit said his bus developed a brake malfunction and he lost control of the vehicle.
The bus hit the woman while she was walking on the sidewalk and dragged her body which was crushed against a power pole.