It varies by event. There may be charter buses from certain "host" resorts, but you'll have to find that out from the event organizers.
When there's anything going on at ESPN Wide World of Sports, Disney also runs buses from 5 resorts: Pop, CBR, and the 3 All-Stars. The buses run once every half hour, and the days & hours of service depend on EWWS event times.
The bus from CBR is less convenient than the others, as it only stops at the Custom House, which is tucked away at one end of the resort. You have to walk or take another bus from your "village" to the Custom House.
Of course, there's never any guarantee that things won't be different a year from now.