However, you can use Bus Lanes on a bike in Sydney, so it is faster than car - if the buses are running any faster. Filtering is illegal and difficult/tight/dangerous on Military road, so don't expect to blast through like you can in London.
Tolls are the same price as cars (I forgot how ridiculous that is), and there are only a handful of all-day CBD bike parks that are always crammed, so it's not a breeze; I've raced to a meeting from the Eastern Suburbs, only to spend 20 mins trying to find somewhere to park (you can park in a metered CBD space for free, but must honour the hours and time limits, which makes them almost useless as 90% are loading zones or short stay during the working day). Private parking don't typically offer cheaper bike rates.
The council try a little (free parking, bus lanes), but it's less bike friendly than London, Paris, or Melbourne. You can do it, as in it's ridiculous with a car, and only "difficult" with a bike.
D