Kirk-Taylor believed the bus was going to stop near where she and Melina's family waited for the 5-year-old, KHOU reported.
Instead, the bus stopped on the opposite side and Melina had to cross the street, KTRK reported.
At the same time, a driver didn't heed the bus' stop sign and flashing lights, speeding past the stopped school bus, according to KHOU.
Kirk-Taylor can be heard on the video frantically telling her daughter to stop.
Despite having a clear video of the car's license plate, police are unable to do anything about it.
Houston Police, according to Kirk-Taylor, said they don't know who was driving the car at the time and they normally have to see the incident in person to be able to issue a citation, KHOU reported.
It is illegal to pass a stopped school bus when its red lights are flashing or its stop sign is extended.
If found guilty, drivers can be fined up to $1,250.
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