We will travel with a group of four. The most ideal scenario ( speaking from a totally naive place), would be to travel to Baia via boat, Pozzuoli by train, then return to Sorrento by boat from Pozzuoli. Is this possible? What might be the best/fastest way to go and return?
The only way to make this connection by ferry is to go...
Sorrento>Ischia>Pozzuoli.
It runs only on certain days. It would take longer than by train. You'd then need a 5-10 min train or taxi to Baia.
Ferry schedule.
http://www.naplesbayferry.com/en/index.
Would cost about 32 E.
To answer the easiest.
Bus to Sorrento. Campania express to Garibaldi. Metro
Garibaldi-Montesanto-Baia.
Total travel time about 2 1/2 hrs. Cost around 20 E.
Timetable Circumvesuvian.
http://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule?bus_route=sorrento_napoli