San Francisco General Hospital spokesman Brent Andrew said six victims still in its care suffer from facial and head injuries as well as fractured ribs, arms and legs. Some have organ injuries.
The patients in critical condition are two men and two women. Two other men are in serious condition. Andrew declined to share any details of a minor who was also admitted to the hospital Friday night.
Twenty people were hurt and at least 30 passengers were onboard when the crash occurred shortly before 3 pm.
Firefighters had to extricate the two pedestrians, who ended up trapped under the bus, and a passenger trapped on the upper deck.
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The driver was conscious and able to speak when firefighters pulled him from the wreckage, Fire Chief Joanne Hayes-White said. But she added it was too early to speculate about what caused the crash.
City Sightseeing San Francisco chief executive Christian Watts issued a statement by email Saturday, saying that the company is "deeply saddened" by the crash.
"We are cooperating with the authorities to determine how this happened. We pray that everyone involved recovers fully and quickly," he said.
At St Francis Hospital, hospital spokeswoman Robin O'Connor said that of three people admitted to the hospital Friday, one man remained in stable condition yesterday morning.
Union Square is one of the city's most popular tourist destinations with several high-end stores, including Macy's and Saks Fifth Avenue, as well as its Union Square Park and skating rink. The scaffolding was in front of what is going to be a new Apple store.
Witnesses said the bus raced across two city blocks, hitting the bicyclist, the pedestrians and striking several moving cars before ramming into the scaffolding. Wrecked cars were scattered up and down the street.
The bus also knocked down several power lines used to propel the city's fleet of electrical buses.
John Zimmer, who works at Union Square Park, said the vehicle never appeared to slow down until it struck the scaffolding. He added that he and others tried to put up a perimeter to keep tourists and others away from the live electrical lines until authorities arrived.