The bus, heading from Los Angeles to San Francisco, flipped on its side Monday evening and slid into a field off Interstate 5 near Fresno. It was carrying 50 passengers.
The suspect, Arturo Martinez, 27, was held on two counts of murder and one count of attempted murder. Authorities said they did not know of any motive.
"He has told us several stories about why he did what he did," sheriff's Lt. Margaret Mims said. She said authorities were checking to see whether drugs, alcohol or mental problems played a role.
Officials said the attack was not related to terrorism, and said Tuesday morning they did not know the motive of Arturo Tapia Martinez, 27, a transient from the Los Angeles area who was booked into Fresno County Jail on two counts of murder and one count of attempted murder.
"There was no clue that there was going to be any trouble on board that bus, Mims said passengers told authorities. "They said he simply got up out of his seat, went up the aisle, and attacked the driver.
"There was no yelling, there was no threats, there was no argument before, just a direct attack on the driver," she added.
"It happened very quickly. He immediately stabbed the driver, too quickly for the passengers to take action on their own," Mims said. "The driver was actually cut in the neck. He struggled, tried to defend himself and lost control of the bus."
After authorities arrived on the scene, passengers pointed out Martinez and he was caught as he tried to run away, Mims said.
"I saw a dude walk fast and pull past to the front (of the bus)," said passenger Howard Johnson, who suffered only minor injuries and later was reunited at a community center with his wife. "I'm feeling blessed."
Twenty-seven people were taken to hospitals, including three in serious condition, officials said. The others were still being evaluated, but most appeared to be in stable condition, nursing supervisors said.
Other passengers received minor scrapes and bruises.
Authorities originally said the driver was one of the two who died, but the Fresno County Sheriff's Department later said that he survived. He was in serious condition.
Jamille Bradfield, a spokeswoman for Greyhound Lines, said a hot line had been set up for friends and family members of passengers to call for information. (See the box to the left of this story.)
"Our top priority right now is taking care of all of the passengers as well as the driver and their families," Bradfield said.
Almost exactly a year ago, on Oct. 3, 2001, a passenger on a Greyhound bus in Tennessee cut the driver's throat, causing a crash that killed seven.
Two weeks later, passengers on another Greyhound bus were credited with averting disaster in Utah after they helped thwart an alleged hijacker. And in November, a Greyhound passenger angry that he wasn't allowed to smoke scuffled with a driver in Arizona, causing a crash that injured 33.
Congress has included $3.85 billion in an anti-terrorism bill passed this year to augment aviation security. By contrast, it has approved $15 million for security improvements on intercity buses.
Dallas-based Greyhound, the nation's largest bus service with 20,000 daily departures, has hired a private company to screen some passengers with electric wands but has inspectors at only a portion of its terminals.