It happened just after midnight on Westheimer at Windchase just minutes after another accident nearby, say police.
METRO police say the 31-year-old man was not in a crosswalk when he was struck and killed. Authorities say it was foggy and that was a factor, as well.
There were four passengers on the METRO bus at the time of the accident. None of them were hurt.
Police say they believed the man was running from a two-car wreck a little more than a mile away at Westheimer and Highway 6.
METRO police recounted the bus driver's story, saying the man essentially appeared without warning.
"The pedestrian appeared immediately in front of him and by the time he did see him, he didn't have time to react," said Chief Victor Rodriguez with the METRO Police Department. "The impact indications and the lack of skid marks indicate that he was going at the appropriate or the marked speed."
The bus has been pulled from the road for a full inspection by HPD's truck enforcement unit and the driver was tested for drugs and alcohol, all of which is standard procedure.
The medical examiner is in the process of notifying the victim's next of kin.
Houston police say at this point, they do believe, based on a witness account, that this is the same person from the first wreck. They believe he ran a red light and fled on foot from the scene.
Authorities also say they found open and closed alcohol beer cans inside the car. They haven't confirmed whether or not alcohol played a factor in the wreck but it is one of many factors they are looking into.