The bus stopped and some passengers got off and rushed to the victim's aid. She received minor injuries.
About 15 minutes later the jogger came back the other way across the bridge. The victim tried to speak to him but he did not acknowledge her and carried on jogging.
Earlier, the Metropolitan Police said that officers had received a "good response" after calling for information on the incident.
A senior source from the bus company Go Ahead London said it was only down to the slow speed of the vehicle that the accident did not result in serious injury.
Putney locals on their way to work yesterday slammed the assault as "despicable".
One woman, who refused to be named, said: "I saw the video last night and I just couldn't believe it, the joggers round here can be a real menace.
"It is despicable. That poor woman, thank God she is okay."
Another resident, a man in his late 20s, said: ''I couldn't believe how close she came to being under that bus.
"Some of the joggers around here can be really rude, but you would never expect that."
Officers continue to appeal for witnesses.
- Additional reporting by Daily Mail