It happened some time after 6 a.m. at Gulf Bank Road and Veterans Memorial in the Hidden Valley neighborhood.
Someone fired a weapon five times toward the bus and at least one bullet struck a rear window, according to Houston police.
Passenger Dwayne Willougby was on board when bullets struck the bus. Willoughby was hit in the head by glass fragments.
"(I was) watching a movie on my phone and heard this 'POW' and see this guy running around the bus," passenger Dwayne Willoughby said. "So, I just dropped to the ground, and then I felt blood trickling. So I got the camera and started looking. I got a little wound on my head and that was it."
Investigators believe the shots came from a passing truck and the bus was not the target.
"I thought it was a rock. Can't be a rock," Willoughby said. "The glass is too tough to be a rock, so it was a bullet. I found the bullet on the ground and the METRO bus glass saved my life pretty much."