I myself have always waited. I have 4 kids & 2 take a bus currently & I see hoe other kids run sometimes to catch it & they can come from any angle.
That said, I would think it would be legal to turn, since you aren't passing the bus.
This question arose this morning when another parent was talking to my wife about it.
I agree with you completely. The bus' red lights and stop sign control traffic going to/from its direction only (yes, even on the other side of a divided highway), not perpendicular to it.
That being said, stopping at an intersection as drawn by the OP exposes the passengers to unnecessary danger simply because of this. For this reason, I would CONSIDER stopping (being seen as stopped and waiting with your turn signal on across the street can lead a pedestrian walking down the diagram to be mislead into thinking the intersection is clear, and being hit by a car traveling left/right misled in the same way; it's all in the situation...). But the bigger problem IMNSHO is that the bus shouldn't be stopping there at all.
In the past (back when I was a passenger), I've seen my bus driver pull out diagonally into the intersection, so he could block traffic in all directions. It was an elegant solution on a narrow road, though it would have you stepping out into the middle of the road on a bigger road where it wouldn't work.
The other solution would be for the school district to simply not allow stops at the intersection. Here's a document from 1992 describing better ways that the school bus should be handling this:
http://www.p12.nysed..._bus_stops.htmlScroll down to "
Proximity to Hazard" and "Intersection Stops"