Can only recommend 'Bikes Only' mate. Got my Suzuki from ACT to Brisbane with them. They would be the most expensive but they are a specialist bike transporter and don't do general freight. I think my enduro bike was $436 to freight in total. If its a bike that you absolutely don't want damaged then this mob are the ducks guts.
I used them very many times when I was in the bike industry, probably moved 150+ bikes with them, and never any problems.