Public bus from Naples to the volcano Vesuvius
The EAV-bus makes a stop at Molo Beverello near the cruise terminal. In the morning there are 2 buses to Capolinea Vesuvia Q.1000, the parking lot near the crater of Vesuvius. There is a bus to Vesuvius at 9h10 and 10h25. Buses drive back at 12h30 and 14h00. The journey takes about 1 hour 20 minutes and costs € 7.30 per person (return).
TIP: From the parking lot it's about 30 minutes on foot to the crater. Wear solid shoes.
From Pompei is a similar service. However, there are six EAV buses in the morning which also make a stop at the Circumvesuviana station of Pompei (opposite the archaeological site). The journey takes just under one hour and costs € 10 per person (return). You can check the timetable here.
There is a third option. Busvia del Vesuvio offers a free shuttle bus from Pompei (Circumvesuviana Station) to the entrance of the Vesuvius National Park. There you have to buy a ticket for € 20 per person (return). From there you continu with a safari truck to the crater at the summit of the volcano. The journey is spectacular.