The colour has an official name
It is called National School Bus Glossy Yellow, a specific hue standardised in 1939, not generic yellow.
Yellow is the fastest colour to detect peripherally
The human eye perceives yellow in peripheral vision faster than red, which is why it was chosen over other high-visibility colours.
One conference set the standard
Frank Cyr's 1939 conference at Columbia University resulted in the first nationwide school bus standards, including the colour.
Myth: any bright yellow would work as well
The specific hue balances maximum contrast against common backgrounds (grey road, blue sky, green trees) with optimal peripheral visibility.