Here are some notes of mine concerning travelling between Pozzuoli and Cumae by bus:
"On the return, if you take the local bus from Cumae to Pozzuoli (not run by SEPSA), you'll travel directly under the ARCO FELICE Roman arch (which is clearly visible from the high point at Cumae), along a road which passes over the beautiful LAGO d'AVERNO (you will see it in its entirety), right past the iron-gated entrance to the GROTTA DI COCCEIO which connected Cumae with Lago d'Averno and Licola (you'll need to stand on the bus to catch a VERY quick glimpse). This bus drops you in central Pozzuoli, by the Tempio di Serapide, from where you can take the no. 152 bus back to Naples (or walk to the Ferrovia Cumana station (in Pozzuoli) or the nearby Pozzuoli Metro Station). A very, very memorable bus ride."
Here is a photo of the northern entrance to the GROTTA DI COCCEIO:
(link may not work)
The entrance to the tunnel is approximately 300 yards due west of the Arco Felice. Therefore, if travelling from Pozzuoli to Cumae, you'll spot the entrance on your left, seconds after passing under the Arco Felice. Conversely, if returning to Pozzuoli from Cumae, the entrance will be on your right, seconds before passing under the Arco Felice. You need to stand on the bus to get a glimpse, since the entrance is partially obscured by trees and bushes.
BTW, the bus which connects Pozzuoli with Cumae, passing along the Via Domiziana on the northern side of Lago d'Averno, and also passing directly under the Arco Felice, is the CTP bus line P12R. The bus runs hourly from Monday through Saturday, and every two hours on Sunday. Here are the schedules:
http://www.ctpn.it/percorsi2.asp?LINEA=P12R (link may not work)
You use the UNICO CAMPANIA zone tickets for this bus route. The Fascia U2 ticket is valid if travelling between Naples and Cumae via Pozzuoli. The 24-hr. ticket costs 3.60 Euros and is valid Monday through Friday AFTER 10:00 a.m. On weekends, it's valid for a full 24-hrs.(Saturday or Sunday), and costs 2.90 Euros. A simple one-way ticket costs 1.80 Euros. These tickets are valid on Naples City Buses, the Naples metro, the Naples funiculars, the CTP buses, as well as the Ferrovia Cumana and Circumflegrea.
www.sepsa.it (Ferrovia Cumana and Circumflegrea)
eavbus.it/export/sites/default/eavbus/orari/… (link may not work)
Another useful product to consider buying is the CAMPANIA ARTE CARD Campi Flegrei, valid for 3 days WITH transportation, which will get you into all six sites within the Campri Flegrei, PLUS one museum in Naples, PLUS other museums at a 50% discount.
You can reach Pozzuoli a number of ways: (i) the Naples metro (from Stazione Centrale, Piazza Cavour-Museo Archeologico Nazionale, Stazione Montesanto, Piazza Amedeo, Mergellina); (ii) the Ferrovia Cumana (from the terminus near the Stazione Montesanto); (iii) City Bus 152; and (iv) the EAVBUS from Stazione Centrale or Piazza Municipio. Note that the Naples Metro and the Cumana rail lines are different, even though they run close to one another