At least before booking Cruz del Sur buses to Pisco online was kind of tricky because the final destination is Nazca. As you, I would ask the recepcionist of your hotel in Lima to call to Cruz del Sur.

Anyway, most people going there take either Soyuz or Flores to cruze de Pisco. Those companies aren't luxury rides but they have very frequent departures. Soyuz has departures every 4-5 minutes and Flores every 15 minutes. Cruze de Pisco is ~5 kms from downtown Pisco and taxi should cost max 10 soles. Of course it's question of personal priorities but often luxury buses depart only very early in the morning while those taking non-luxury bus late in the evening can spend the night sleeping in bed. From Lima it's 3,5-4 hour ride to Pisco.