bus and train from Naples to Pompeii and Herculaneum

I am not sure why you would want to since the the Circumvesuviana trains run to Pompeii Scavi at the entrance to the Pompeii site, and to Ercolano Scavi, which is Herculaneum.

https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

I believe that it is, but the bus may not be a SITA (public) bus. Most people would take the Circumvesuviana for both ends of your trip. It would help if you gave the month of the trip, and made it explicit that you are sleeping and leaving your luggage in Naples for the ancient sites. Why do you want to start on a bus? The sightseeing value is modest. This is a suburbanized area, with a few quick views of the coast.

Circumvesuviana tickets are undated and not for named stations, but zoned. If you are afraid you will mix up the short distance and long-distance tickets, write on the back when you buy them. An extreme solution would be to buy three tickets "to" Pompeii, and use them for all three journeys. (Not recommending that, just trying to describe the system, which is like New Jersey Transit busses - zoned fares.) They can be bought from a human attendant on the lower level of the Naples main train station, or from newsdealers who know all the tourist questions, believe me!

The Circumvesuviana is more like a commuter train or a Metro than like the long-distance rail network. You need three tickets per person for the trip you describe (all by train, I mean), and you validate the ticket in a machine on the platform before your train comes. Herculaneum is a substantial downhill walk from the train station, unlike Pompeii. There is actually a five-ancient-site ticket (good for three days), but you have chosen the, by far, top two. That's fine.

Only Pompeii has food inside. You can't re-enter the sites if you exit them to go out and eat.

Perhaps the OP is talking about the CitySightseeing shuttle bus from Naples to Pompeii:

https://www.city-sightseeing.it/en/shuttle-bus-naples-pompei-vesuvius/

In answer to her question, yes, you can ride it one-way from Naples to Pompeii, and then take the Circumvesuviana commuter train back to Naples, stopping at Herculaneuam along the way. The bus is more expensive, but you're guaranteed a seat and air conditioning--plus there aren't any pickpockets.

Thank you, Just what I was looking for!