Greyhound has no bus service to speak of in Aust.
Plenty of buses, not necessarily called Greyhound, up and down the east coast - a heavily travelled backpacker route. It's that Victoria thing, you know. Even the buses don't go there
I can offer spare room, with ?OK sofa bed.
When you firm up your time, we'll look at detail. Do you eat the same sort of food as Penny the Hamster - i.e., lettuce? Or something more! She's my only experience of a US guest. Had plenty of Swedes - they eat anything and everything!