Santiago to Sienna

Sienna is in the other direction from Santiago. When you leave the pilgrim office in SJPdP, make your way to the main street and turn right. Its only about a thousand kilometers so not much more as if you pedalled from SJPdP to Santiago.

Have you considered the Via Francigena route?
http://www.urcamino.com/via-francigena/route

Assuming you want to take the train (instead of simply cycling to Siena from Santiago) you have plenty of options.

There is an discussion about getting back to Italy from Saint Jean you may to check out:
http://www.caminodesantiago.me/community/threads/how-to-get-to-sjpp-from-italy-by-train.22662/

Siena on the main train line from Florence to Rome, so if you want to train there best to make your way to either Torino or Milan or Florence via France and Spain.

One approach is to catch an overnight train to Barcelona from Santiago and then make your way along the Spanish/French/Italian coasts to Torino.
This might be more scenic but it might require more work with connections, etc

Another approach is make your to Paris and then catch an overnight train to Italy probably to Florence and then catch the one of day trains into Siena.
You could take the train to Madrid and then the overnight train to Paris, spend the day sightseeing in Paris and then catch the overnight train to Florence.

There is now an overnight train from Barcelona to Paris too - just about to open.

Or you could fly to Milano or Bologna and train to Siena.

Alternatively you could fly with Ryanair from SdC to Milan Bergamo and take the train / bus down from there.

There's an excellent site run by a British railway man giving advice about rail travel, how to book, routes, ticket types, facilities on trains, prices etc. Seat61.com. Named after his favoutite seat on Eurostar. Not a booking agency, just a useful resource for travellers.