There is no "one seat ride" between Siena and Sorrento, and there's no clear "winner" among the transit options, so you'll have to look at the various options and choose which one is least painful for you.
Sorrento is accessible by bus or by a private train line (the Circumvesuviana) from Naples, as well as by boat from Naples and some Amalfi Coast destinations (in season). It is not on the main Italian Trenitalia system. Siena is on the Trenitalia system, but on a spur line, so getting to most places by train requires at least one connection; it also has a good amount of bus service. However, in Italy, buses mainly fill in gaps in train service, and connect places with limited or no train service to the larger hubs in their region; they rarely go between regions. For these reasons, these destinations simply don't have an easy connection between them.
A North American equivalent might be getting from Cape Cod to Niagara Falls without a car; you're going to have to take more than one conveyance to do that.
Do look at Rome 2 Rio to see your options: http://www.rome2rio.com/s/Siena/Sorrento-NA-Italy