Civitavecchia is the main port town for cruise ships and ferries leaving for the Mediterranean & N. Africa and is nearby to Rome.
Chris, I took that same journey this past June.
Siena is one of those towns where the bus station is right next to town - even the train station is reached by bus. You could take a bus to the train station, then train to Rome and then onto Civitavecchia. However, I discovered a different route because it saved us a layover, I think. Siena - Grosseto by bus (it lets you off at the train station). Then hop on any of the lines that run down the coast to Civitavecchia train station. Take a bus or cab to the port (don't walk, trust me), there you are.