There is not direct connection between Paphos and Larnaca. However, you can use the intercity bus from Paphos to Limassol and then catch the intercity from Limassol to Larnaca. At Limassol, you change buses at Saint George Havouzas. You will have to wait for the bus that goes from Limassol to Larnaca.
Duration: Paphos-Limassol: 50 min, Limassol - Larnaca: 50 min, average waiting time in Limassol: 40 min. Total time: 140 min

From Paphos to Limassol
The route: Karavella bus station (starting point), Pafiako stadium (oppossite Debenhams), Kianos Stavros (opposite McDonalds), Saint George Havouzas, Old Limassol Port, New Limassol Port.
Departure times from Karavella
Monday to Friday: 06:00, 07:30, 08:30, 10:00, 12:00, 13:00, 14:30, 15:00, 16:30, 18:00, 20:00
Saturday and Sunday and Public Holidays: 08:00, 10:00, 12:00, 14:30, 16:00, 18:30
From Limassol to Larnaca
The route: New Limassol Port (starting point), Old Limassol Port, Saint Raphael Hotel, Chirokitia, Xidias, Old Larnaca Hospital, Finikoudes.
Departure times from New Limassol Port
Monday to Friday: 06:00, 07:30, 10:00, 13:00, 14:30, 16:00, 18:00, 21:00
Saturday and Sunday and Public Holidays: 08:30, 10:30, 11:30, 14:30, 16:30, 19:00
Intercity bus from Larnaca to Paphos
You first travel from Larnaca to Limassol and then from Limassol to Paphos as descripted above.
Duration: 140 min
From Larnaca to Limassol
The route: Finikoudes (starting point), Old Larnaca Hospital, Xidias, Chirokitia, Saint Raphael Hotel (Limassol), Old Limassol Port, New Limassol Port.
Departure times from Finikoudes
Monday to Friday: 06:00, 07:30, 10:00, 13:00, 15:00, 16:00, 18:00, 20:30
Saturday and Sunday and Public Holidays: 08:30, 9:30, 10:30, 14:00, 16:30, 19:00
From Limassol to Paphos
The route: New Limassol Port (starting point), Old Limassol Port, Saint George Havouzas, Kianos Stavros, Pafiako stadium, Karavella bus station.
Departure times from New Limassol Port
Monday to Friday: 06:00*, 06:10**, 07:00**, 07:30, 09:30, 10:30, 12:30, 14:00, 15:00, 16:00 17:30, 18:30, 20:00
Saturday and Sunday and Public Holidays: 08:00, 10:00, 12:00, 14:30, 16:00, 18:30
Another convenient way to travel from Limassol to Paphos airport is Travel express. Travel express buses depart every 30 minutes starting at 06:00 and ending at about 18:00. The cost is 9.50 €.