Although Zagreb is a city that is not in near vicinity of Korcula, due to the fact that Zagreb is capital of Croatia and introduction of cheap flights to Zagreb (couple years ago by WizzAir and recently by EasyJet), people sometimes fly there, instead to Split or Dubrovnik which are Korcula’s nearest airports.
There are several options to reach Korcula from Zagreb:
The first option is to take a bus from Zagreb to Split and then take any of the ferries from Split to Korcula or Vela Luka. This option is probably the easiest one; however, due to flights arrivals, this option is sometimes not suitable.
The third option is to take a direct bus from Zagreb to Korcula, the one that goes daily to Korcula Town and Vela Luka. This option is bit awkward as journey lasts all night, departing around 19.30 hrs arriving in Korcula following morning at 06.45 hrs.
All these buses are in operation every day so they are pretty reliable means of transport. All buses and ferries are comfortable and air-conditioned, and there are some great views of rivers and mountains as well as the islands and bays while travelling on these routes.
And finally, there is always an option to take flight from Zagreb to Split or Dubrovnik, the route that Croatia Airlines runs daily, few times a day and from there, take bus or ferry to Korcula.