How can I travel from Jorge Chávez International Airport (LIM) to Paracas, Ica by public transport when my flight arrives at 14:45?
It will be on a Friday if this matters.
You can reach a comfortable regular bus company like ExcluCiva, Cruz del Sur, Oltursa and Peru Bus (Soyuz). The latter being the most inexpensive. They have bus stations in Lima, Paracas, Ica and Nazca. They also have connections to Arequipa or Cusco (and towns in between) although sometimes the schedule is not always met. Peru Hop offer direct buses to and from Lima daily they include a pick up and drop-off service.Also there are minibuses to Ica, which are a bit cheaper and provide hotel-to-hotel service. Cheaper bus companies only go to Pisco, from where you can get a taxi to Paracas (S./15 for two Apr 2015).
Peru Hop a new service offer daily direct buses to the centre of Paracas to or from Lima and Huacachina.
Here is an example from Oltursa:
Andrea A on TripAdvisor wasn't very happy with ExcluCiva but they are not likely to be any worse than the alternatives.
Google Maps suggests 30 minutes by car from Jorge Chávez International Airport to Avenida Andrés Aramburú.
Connection in Ica (city) may mean a long wait:
The alternative might be to spend Friday night in Lima and catch an early bus the next day.