Video footage from May 5 showed a male jogger knocking the 33-year-old woman onto the road as she walked across Putney Bridge on the River Thames.
The bus is seen swerving and narrowly missing the woman.
Police said the victim suffered minor injuries and passengers on the bus came to her aid.
The jogger returned 15 minutes later as he made his way back across the bridge but did not acknowledge the victim when she attempted to speak with him, according to police.
A 41-year-old was arrested Thursday morning on suspicion of causing grievous bodily harm at an address in the affluent Chelsea area, a Metropolitan Police statement said.
But lawyers for Eric Bellquist said in a statement Friday that their client has a clear alibi.
"Our client has been wrongly implicated in this matter; he categorically denies being the individual concerned and has irrefutable proof that he was in the United States at the time of the incident. Consequently we expect a swift resolution to this wholly untrue allegation," Duncan Lewis Solicitors said in a statement.
Officers received "a good response" from the public after releasing the footage, police 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," said Sgt. Mat Knowles, the investigating officer from Putney Safer Neighbourhood Team, in an earlier statement.
This story has been updated to reflect the latest information from police about the suspect's age.