It seems some posters are offering suggestions on how to get TO Raspberry Flat but you are interested in working out how to get OUT. Bit different. Presumably you don't know exactly when you will finish and have the trip in sorted.
Maybe have a chat to anybody you meet on the way out (eg on the trail or at Aspiring Hut) and ask for a lift. Short of that the Rob Roy Track is very popular with day trippers so there should be even more people to meet near the carpark. Maybe have a wash in the river beforehand...
When are you heading down? I am going down from ChCh next Friday for a week with my wife - if the deep low in the Southern Ocean decides to get the hell out of the way and wake room for the High sitting over The Bite.