The mother, with two children, was dealing with one who was misbehaving when she realised the other had gone.
She shouted after him and another passenger went after the suspect and retrieved the boy from her.
The alarm was raised by the driver but detectives have not heard from the mother and are keen to speak to her.
The woman who allegedly tried to take the boy is in her 40s and of Chinese appearance, a police spokesman said.
He added the incident was being treated as potentially very serious.
Anyone who witnessed the incident on the no 90 bus which had come from Marksbury Road and was stopped near Wilkinson's store on East Street at 1430 GMT on 16 January, is asked to contact police.
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