After few guests enquired me last season I did a small research and now publishing here.
There are several ways to head to Pompei from Rome and they are by bus, by train or at least by private shuttle van but I’m actually going to exclude this last one that will cost you a fortune and examine the first two options.
By private coach tours
I had a guest years ago travelling on a budget, she booked the bus ride on Expedia without the tour guide option. That is convenient as you’d be able to rent an audio guide at the entrance and do the tour yourself.
By private bus
At stazione Tiburtina (you can get there from here taking the 492 – Tiburtina direction – and getting off at the Terminus). Out of the station there is a big bus station, you have to take Marozzi line going to Sorrento, it’s departing every day on Summer season at 7 – in Winter season just on FRI SAT SUN. It takes three hours to Pompei. The trip back departs at 5.45 and you’ll be back in Rome at 9.
By Frecciarossa (high speed train)
Trains to Naples depart from Termini almost every hour, it takes 1:10 but round trip start from €40. Arrived in Naples go upstairs and take the Circumvesuviana train line to Pompei.
By Regional train
That is a very convenient option, you have to take the train to Formia and then the metro train to Pompei. On the way back you get the Circumvesuviana train to Naples and the regional train to Rome. Each way cost €13.20 (actually late 2013) but each trip take more than 3 hours. Please check the attached pdf timetable: rome – pompei budget train roundtrip