Trenitalia operates a train from Polignano a Mare to Matera hourly. Tickets cost $3 - $8 and the journey takes 32 min. Ferrovie Appulo Lucane also services this route hourly. Alternatively, Marozzi VT operates a bus from Polignano a Mare to Matera hourly. Tickets cost $9 - $11 and the journey takes 45 min. FlixBus also services this route 3 times a day.
From Polignano A Mare train to Bari Centrale then train to Matera Centrale. 2 h 33 min 10€. From Polignano night bus to Bari then bus to Matera. 2 h 55 min 13€. From Polignano a Mare taxi to Matera. 1 h 13 min 99€. From Polignano a Mare drive to Matera. 1 h 13 min 10€.