"The bridge had been closed in both directions, and that is changing as the clean up continues. "One north bound lane is open but we are still advising people to stay away.
"Given you usually have four lanes, traffic is incredibly heavy."
Firefighters were called to Milsons Point just before 5.30pm, after the bus burst into flames.
The cause of the blaze is yet to be determined.
The 30 passengers on board made it safely off the bus, however, a New South Wales Ambulance Service said three were treated for minor smoke inhalation.
All three were taken to Royal North Shore Hospital for further treatment.
A Fire and Rescue NSW spokesman said four fire crews were called to the scene but had trouble getting to the bus due to the traffic congestion the incident had caused.
He said the fire was extinguished soon after they arrived on scene and the burnt wreckage had since been removed.
A small amount of oil remains on the roadway and requires further clean-up, he said.
Passengers had to be evacuated and left the bridge on foot before firefighters arrived to extinguish the blaze at 5.35pm, The Daily Telegraph reported.