Olivier Salbris swerved his bus around the woman after a jogger pushed her into the path of his double-decker on Putney Bridge in southwest London.
In the seven months since, detectives have arrested and released three men, but have still not identified the jogger they are hunting.
Mr Salbris, 45, said He should come forward and talk to the police. He has done something bad and the consequences could have been terrible for the victim and me.
It would be good if the police could catch him, but if only he could reproach himself, search his conscience, at least be responsible for his actions.
The driver was heading south across the River Thames on Putney Bridge at 7.40 am on 5 May when he saw the jogger apparently deliberately shove the woman as he ran past her.
The dramatic CCTV footage has been viewed on the internet by millions around the world.
The victim fell backwards with her head in the road, in the path of Mr Salbris’s number 430 bus, and only inches away from his front wheel.
His quick reactions meant he managed to swerve around her without colliding with other vehicles in the next lane.
I don’t know why the jogger pushed her, perhaps he was having a bad day and decided to push the first lady he saw. It could have been personal, too, said Mr Salbris.
I really don’t know how someone could do something like that to somebody else.
The unidentified woman, who was 33, was shocked but not seriously hurt and was able to talk to police.
Mr Salbris spoke to her and gave her his details as she recovered before reporting the assault to his bosses, but has not had contact with the woman since.
I’ve heard nothing from her, unfortunately, he said. I really wish that she is well, but I don’t know the reason why that happened to her.
Police said the jogger ran back across the bridge, heading north, 15 minutes after the assault, but ignored his victim’s attempts to talk to him.
He is described as in his 30s and wearing a light-grey T-shirt, dark blue shorts and grey trainers. He had short brown hair and brown eyes.
Last month Mr Salbris was given a special commendation for his life-saving reactions at the annual UK Bus Awards.
The Metropolitan Police said local detectives were still investigating the assault and were still hoping for a breakthrough.
Anyone with information is asked to call police or ring Crimestoppers anonymously on 0800 555 111.
News Source SkyNews