The 50-year-old male was arrested on suspicion of causing grievous bodily harm after being held at a Chelsea house on Thursday.
He has been released but the investigation continues, according to British police.
British police appealed for witnesses to help find the man.
London's Metropolitan Police Service released surveillance camera footage on Tuesday of the incident that occurred in May.
It shows a jogger in shorts and t-shirt banging into a pedestrian, who tumbles in front of a double-decker bus.
The bus swerves to avoid hitting her.
Sergeant Mat Knowles said "it was only due to the superb quick reactions of the bus driver that she was not hit by the vehicle."
Police say the woman saw the jogger running back across the bridge about 15 minutes later and tried to speak to him.
