His lawyer yesterday issued a denial of the allegations against him, claiming he was out of the country at the time.
Mr Bellquist, a top boss at the Wagamama and Byron restaurant chains, says he has "irrefutable proof" he was in the United States at the time of the incident, which took place at 7.40am on May 5.
In it, we see a man jogging on the side of the bridge when he suddenly pushes a passing woman to the ground, putting her in the path of a coming bus.
Bellquist's profile on Hutton Collins Partners's website is still up.
On Monday, CCTV footage was released showing the woman, 33, narrowly avoiding serious injury when she was pushed into the path of an oncoming bus by a jogger on 5 May.
The bus stopped and passengers tended to the woman following the incident at about 7.40am on May 5. He runs past a pedestrian before appearing to shove the woman onto the road as the bus arrives.
The Met said he will face no further action.
Police had appealed for the man to come forward to speak with them after publishing CCTV footage of the incident.
Police described the jogger as a white man, aged early to mid 30s, with brown eyes and short brown hair, wearing a light grey t-shirt and dark blue shorts.
Some 15 minutes later, the suspect passed his victim again on the bridge, going the other way.