Honestly, I'd shoot for 12:15 or 12:30 from Downtown Disney. Bus service is notoriously slow. It - specifically the PI/WestSide stop - is also where drivers tend to change shifts. That can slow you down even further. Also, your assigned DME pickup time is when the bus leaves your resort - not when it gets there.
Anyway, though - you don't want to be stuck sitting on a bus at Downtown Disney waiting for the new driver when your DME bus is loading at Pop. Err on the side of caution.