Is there bus service from Orvieto to Siena

You can take the train (1 change), one leaves at least every two hours.

I don't believe there is a bus (but will stand corrected).

As far as I can see you would have to take a bus to Perugia and from there to Siena and it would take about 4 hrs. Train is more direct and takes about 2-1/2 hrs.

Alice, you can take a train from Orvieto to Siena, with a connection in Chiusi. Takes from just under 2 hours to about 3 hours, depending on the schedule. The train would arrive a small distance from central Siena, likely then requiring a taxi or local bus into town. On this route you could also make a nice mid-way stop in Montepulciano for a while, maybe for lunch. One of the reasons a bus would be more difficult and circuitous is that Orvieto is in Umbria and Siena is in Tuscany. Another longer possibility would a train from Orvieto to Florence, then a one hour bus into central Siena.

Alice,

Zoe and Larry are right, your best option is taking train(s) as the bus takes 4 hours.

Check this website to see different options to get from point A to point B : http://www.rome2rio.com

Safe travels!