Security footage contradicts the claims of a mother that she was kicked off a bus in Mandurah because her baby would not stop crying, Transperth says.

An investigation into the incident that allegedly occurred on Tuesday found "a number of significant inconsistencies" between the mother's story and the CCTV vision of the incident, Transperth spokeswoman Claire Krol said.

Significant time and resources were invested in examining the allegations including reviewing CCTV footage, interviewing the driver and speaking with the passenger involved.

"The investigation has identified a number of significant inconsistencies between Casey Nelson's recollection of the bus ride and the CCTV vision of the incident," she said.

Ms Nelson had said she was embarrassed when she was kicked off a bus while taking her six-year-old daughter to school, because her one-year-old son was crying.