Personally? What I would not do is a bus tour from Rome. They spend abt. 6 hours of road time (3 each way) for an average of just a couple of hours at the scavi....which is HUGE and benefits from more time. With a bus tour, your time is not your own; you need to be back on the bus when the tour is over.
High-speed train to Naples and then local Circumvesuviana commuter train to the site is the way to go, IMHO. Covering the bulk of the distance by 'fast' Trenitalia or Italo train shaves off some serious time. The Circ. commuter is a battered, un-lovely, un-airconditioned thing but it's cheap and gets the job done. You do want to keep a tight hand on your valuables when taking that one but heck, you want to do that on ANY sort of non-reserved public transit so no big deal.
You would take a 'fast' train to Napoli Centrale, and walk inside to the attached Napoli Garibaldi station; that's where you'll get the Circumvesuviana. You'll buy your tickets for that one at the station, they'll cost you just a few eruo, and you'll want to make SURE to validate them before boarding. You'll take the train to Pompei Scavi - Villa dei Misteri; the station right in front of the main entrance to the scavi. To go back to Naples, reverse the process. Below is a link to the current Circumvesuviana schedule; it's about 30-40 minutes between Pompeii Scavi and Naples. It's about 70 minutes by fast train from Naples to Rome; use the Trenitalia or Italo websites to explore your ticketing/timing options.
https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule
Guides: Mondo Shared Tours is a Rick Steves endorsed business that has seen many good reviews from posters who have used them plus they're very economically priced small-group tours. You'll meet your guide at the scavi, and when the tour is over you can do some more exploring on your own before heading back to Rome.
https://www.sharedtours.com
If interested in doing it this way, we can provide some greater detail on the hows but it is not difficult; lots of folks take it on themselves. :O)
https://www.trenitalia.com/en.html
https://www.italotreno.it/en