Which is better ? Bus or train from Naples cruise port to Herculanium

To be honest, I am not aware of any direct bus or train to Herculaneum from the cruise port, the only route by public transportation is the bus or maybe the metro to the main train station area, Piazza Garibaldi, and then taking the Circumvesuviana train to Ercolano Scavi station, and then walk.

Alternatively, you could take a taxi to the station (or to the ancient site), negotiate with the driver. If a group, you could look at some type of tour service.

google maps shows a distance of ~ 14 km ( 8.3 miles) so a taxi may not be unreasonable

https://www.google.com/maps/dir/Molo+Carlo+Pisacane,+Piazzale+Molo+Carlo+Pisacane,+1,+80133+Napoli+NA,+Italy/Herculaneum+Ticket+Office,+Ercolano,+Metropolitan+City+of+Naples,+Italy/@40.8246016,14.2721777,13z/data=!3m1!4b1!4m19!4m18!1m5!1m1!1s0x133b0847693f0b63:0xb3d2abedc2433627!2m2!1d14.2628714!2d40.8442015!1m5!1m1!1s0x133ba6e91f9b4eff:0x39f1005c58b3ea57!2m2!1d14.3473439!2d40.8046617!2m3!6e0!7e2!8j1759827240!3e0!4e1?entry=ttu&g_ep=EgoyMDI1MTAwMS4wIKXMDSoASAFQAw%3D%3D

Month of year?

Do you mean the cruise ship’s proprietary bus tour, which guarantees the ship will not leave without you? Ancient sites shuttle from Pompeii?

Circumvesuviana is cheapest, but has a 10-15 minute downhill walk from the train station. Have to get to Naples train station, of course. What are your lunch plans? No food inside, no same day readmission .