Traveling from Orvieto to Siena

Trains won't be a problem if you don't find a bus. In Orvieto, the funicular station is across the street from the train station; at the top of the funicular route are small buses to take you to the center of town (bus is free with your funicular ticket). In Siena the train station is about five minutes by taxi from the center of town, and there are also city buses at the train station that go to the historic center. The TI at the train station in Siena is very helpful, will check bus route numbers for your hotel.

Larry, Which hotel are you staying at in Orvieto? It's very easy to walk from many hotels to the Funicular station and then take the short trip down the hill directly to the station. While the station may be somewhat "outside of town", it's extremely easy to get to! When you arrive in Siena, it's also very easy to take a Taxi or Bus up to the town. The trip is only a few minutes. One of the quickest trips is a departure at 10:15, arriving Siena at 11:57 (time 1H:42M, with a 5 minute change at Chiusi-Chianciano Terme). I believe there is a Bus on that route, but that's not a method I normally use so would have to do some research. Happy travels!

Thank you Zoe and Ken. So far, it does not seem there is a bus. I just thought a direct bus might save a little time and hassle at the beginning, middle and end of this short trip, but no big deal if none exists. That may have something to do with Orvieto being in Umbria and Siena in Toscana, who knows.
I am staying at the Hotel Virgilio right by the Duomo in Orvieto. I've seen that there are some train schedules that make the trip a little faster, but those schedules don't fit my needs that day. There's a regional train leaving at two something that will suit me, unless someone initiates a bus line twist now and then, not very likely I suppose.

Larry, Even if there was a Bus, it's likely there would only be one or two departures per day, which could vary between work days and weekends. If you're looking for a particular departure time, Bus would not be a reasonable option. If you want to leave Orvieto about 14:00, the 14:21 departure should be good. As the trains are Regionale, DON'T forget to validate your tickets prior to boarding the train on the day of travel, or you'll risk hefty fines! In that situation, I'd buy my tickets upon arrival in Orvieto, since I'd be at the station anyway. I've found from past experience that it's not always a good idea to try and buy tickets on departure day. Although Hotel Virgilio is a bit farther from the Funicular, you should still be able to walk.