Easiest would be to take a taxi from the airport to the bus terminus, which is on the other side of the city. (be prepared to pay for that privilege though) Plenty of taxis as you exit the airport. Then take the Greyhound or similar to Nelspruit. You can book your bus ticket online in advance, or your sister can buy you one from any Computicket outlet, like at Shoprite.
What good am I, if I know and donít do, If I see and donít say - Bob Dylan