Are bus drivers supposed to stop if your sitting?

If we're talking Metro in DC, they can be late, but they can't be early to a stop. The driver may not have seen you, or, more likely if we're talking one of the S line on 16th Street during rush hour, the driver already had them packed like sardines and couldn't pick up any more passengers.

If they don't see you out there at the scheduled time, they drive by. If you are sitting, you aren't visible. He is indeed on a time schedule. He has other kids to pick up, and has a time frame to be at the school to drop you off.

The driver has no way of knowing if you're waiting for the bus or just resting your feet unless you stand up and look like you're waiting for the bus.

They are only required to stop if it is clear someone is waiting for the bus, or they are ahead of schedule for a TIMED stop. Not all stops have a scheduled time, and sitting at the bus stop doesn't indicate you are waiting for the bus.