The Met Police said Two men, both aged 41, who were previously arrested have been released without further action.
The hunt is still on for the man for suspicion of causing grievous bodily harm.
The search comes after CCTV footage was released that showed the woman, 33, narrowly avoid serious injury due to the bus driver's quick reactions.
The suspect is in custody at a south London police station, the Met said.
The force said it had received a "huge response" to its appeal for information.
CCTV showed the incident when a man running along Putney Bridge in west London and appearing to shove the 33-year-old into the road when she was walking towards Putney Bridge Tube Station.
The oncoming bus is forced to swerve into the adjacent lane to avoid hitting her.
Sgt Mat Knowles said: "It was only due to the superb quick reactions of the bus driver that she was not hit by the vehicle."
The Metropolitan Police said the bus stopped and passengers tended to the woman - who received minor injuries - following the incident on the morning of 5 May.
Officers said the jogger ran the other way across the bridge around 15 minutes later and the victim attempted to speak to him, but "he did not acknowledge her".
Sergeant Mat Knowles, the investigating officer from Putney Safer Neighbourhood Team, said: "The victim was put in extreme danger when she was knocked into the road. It was only due to the superb quick reactions of the bus driver that she was not hit by the vehicle.
"We are keen to speak to the jogger in the CCTV about what happened that morning. We would urge him or anyone who recognises him to get in touch with us as soon as possible."
Anyone with information or any witnesses are asked to call Putney Safer Neighbourhood Team on 020 8785 8874 or 101