Witness Vanessa Kenley told the court she saw Campbell after he had got off the bus shouting "long live Palestine" and "long live Gaza" in the street.
She said she had subsequently recognised him from press reports of the incident.
Prosecuting solicitor Katie Weiss said the incident had been brought to the attention of London Mayor Boris Johnson and Labour Party leader Ed Miliband.
Campbell was released on court bail on the condition that he does not to travel on the 102 bus route between Golders Green and Henleys Corner, in north London, or contact JC journalist Rosa Doherty, who was travelling on the bus and witnessed and reported the incident.
An assessment will be made to consider the fact he suffers from alcoholism and mental health problems.
He is due to be sentenced on October 31.
