We were in Amalfi in Sept, and I had been looking to see if I could take a ferry from Amalfi to Naples to bypass the bus/train combo...no can do...at least not until Sorrento (Edit - oops - no direct ferry from Naples to Amalfi). That being said, you'll have to use the bus between the towns on the Amalfi coast. I'm not sure if a day will be enough to see it all by bus. We had 3 nights near Amalfi (in Atrani) , and didn't see all I'd hoped we would. We used Sorrento Silver Star car services and had a private tour for one day, and even then, with all the driving (and skipping Amalfi since we could just walk there from Atrani), we spent about 60-90 min each in Ravello, Sorrento and Positano, a few stops for scenic views, and it was STILL an 8 hour tour!
Amalfi was OK - but after seeing the church and walking up the main road, that was enough. Ravello was gorgeous (especially the Cimbrone Gardens). We didn't see much of Sorrento but the city center, and by the time we did Positano it was so hot, we didn't walk around to much, but it looked gorgeous and I wish we had spent a little longer. Can't speak for Salerno.