if I put a stop sign somewhere is that legal? or there's some statute (or at least local ordinance) that says that yellow buses on this and this route can have moving stop signs?
Yes, in the US, school buses come equipped with a stop sign that they extend when stopping to let kids on and off the bus. You (as a driver) are required to stop (and not pass) on both sides of the road while the bus has their sign extended.
https://www.mass.gov/info-details/mass-general-laws-c90-ss-1...