Is it possible to take a bus from Sorrento to Paestum?
Yes, but you have to do it in 3 hops: Sorrento to Amalfi, Amalfi to Salerno, Salerno to Paestum. You can also take the Circumvesuviana train from Sorrento to Naples Centrale station, then a "regionale" train from Naples to Paestum.
Paestum can be awkward to get to from Sorrento. From about May to end of October there is a weekly organised tour from Sorrento which also visits Salerno on the way to Paestum. If you do not feel up to the journey by public transport it is a good second choice. Have taken it myself and it is not bad. http://www.goldentours.it/en/salerno_e_paestum.php
When my husband and I made the trip, we rented a car. We could have taken the train to Naples and from there to Pasteum but we would have had a 4 hr time frame for Pasteum, which is way too long. We were there for about 1 hr (including the museum), so be sure to look at the return times from Pasteum to Naples to ensure you aren't there too long.
Well, some think Paestum has one of the best collection of Greek temples anywhere, and 1 hour would not be sufficient for them.
I did a day trip from Sorrento to Paestum in 2008. I took the bus to Amalfi, spent time exploring Amalfi, and then took a bus to Salerno. I took the bus from Salerno to Paestum, but in retrospect would take the train. On the way back, I took a train from Paestum to Pompei, walked (taxi or bus are also an option) from the train station to the Pompeii Scavi Circumversuviana station, and took the Circumvesuviana back to Sorrento. It was a very long day, but both Amalfi and Paestum were worth visiting. If you buy the Campania ArteCard, the entire trip MAY be covered by the 3-day Campania Pass you receive, but I found it very difficult to find anyone who actually knew what means of travel the pass covered.