The Thurs-Sun thing is not really reliable. They pretty much run only when there is something scheduled at EWWS.
At CBR, the EWWS bus stops only at the Custom House, at the internal shuttle stop. You would get off your incoming bus at Barbados, and walk the path across the street to the Custom House.
At Pop, the bus stops at the stop nearest the lobby. I don't think they've put up a sign yet; it may just say "Bus Only". At all 3 All-Stars, the stop is the furthest from the lobby, shared with DHS.
If the buses are not running, Pop is the closest resort, so the cheapest place to grab a cab.
To the OP: you're fortunate that you're within easy walking distance of the MK. Guests at most other resorts have to take 3 buses: a 2-hour Odyssey. Even so, allow plenty of time, as the EWWS buses run only every 30 minutes.
Direct charter buses may or may not be available. It's up the event organizer and/or sponsor.