Police in Olympia, the state capital, said they identified Kiel Duggins, 24, from the videotape, KOMO-TV in Seattle reported. Duggins was arrested at a downtown transit station soon after the attack Tuesday.
Duggins appeared at a hearing Wednesday and was ordered held in lieu of bail.
The videotape shows the Intercity Transit driver telling a man to leave because of his bad language. After the driver pulled the bus over, the man eventually went towards the door but then refused to get off and the driver tried to shove him out.
"If you hit me in the face, we will fight to the death," the man said at one point.
A passenger tried to intervene but was unable to get the man off the driver. Once the man did leave, passengers and the driver called for help.
"These incidents, I'm very happy to report, are very unusual," Kris Fransen, a spokesman for the bus operator, said. "Our drivers are very well trained in self-defense. They are trained how to take action to protect themselves and our passengers."