cogs
bruce is definitely on the right track
I believe that in NSW potentially your swiftest/cheapest path would be to rely on s. 97 of the Victims Rights and Support Act 2013, which empowers the court to order any person convicted of an offence to pay compensation to any "aggrieved person". Link to the legislation here:
http://www.austlii.edu.au/cgi-bin/viewd ... 8/s97.html
Getting such an order is best done by application made at immediately at the conclusion of any trial or guilty plea. The power only exists if a conviction is recorded: beware the judicial officer who decides that although the offence is proven no conviction should be recorded because the driver is such a nice person usually.
Of course, having the chance to make the application relies on your having notice of any hearing and being able/prepared to set aside the time to be there. You may turn up one day, only to find that it's adjourned off to some other time. Yes, the system works fine for those who are paid to be there, not so well for everyone else.
If you're a witness at the hearing you should have the opportunity to tell of your losses while giving evidence, and you'll get witness expenses in some limited amount.
Alternatively, you can go the civil route via letter of demand and small claim, as jules has suggested.