To clarify one doesn't buy an Opal card nor does a retailer sell an opal card as they are free. I've heard of AirBnB hosts saying the cards have a cost which guests need to cover - this is not true. The Opal card is free and widely available in the inner city.
You obtain an Opal card and then load it with value, for adults the minimum load is $10, the next value which can be loaded is $20.
Three great features of Opal:
1. $2.50 all day Sunday travel in the NSW greater metro area from Nowra to Dungog to Scone to Goulbun
2. Transfers on the same mode charge one fare for the total distance not multiple fares for multiple buses
3. The one hour transfer, allowing you to break your journey for up to an hour, or as I do make my journey, get what I need in around 45 minutes, and then return home which mean I only pay the minimum bus fare of $2.10
As for the journey from Darling Harbour to Bondi it depends on where in Bondi. If the junction walk to Town Hall railway and take the train. If Bondi Beach take the bus - 333 or the 380. The very long but oh so lovely 389 goes to North Bondi and the Junction but not Bondi Beach or Bondi Road. All three services travel along Elizabeth Street, catch them across the road and down a bit from David Jones'.
If you're staying on the western side of Darling Harbour you could also take the tram to Central railway and from there take the ESR to the junction but that total journey would be most expensive.
The suggestion on avoiding the gate fee and the route 400 seems odd and gee a massive time suck. Just take the train.