Hello stephencook5,
There are Siena to Rome buses if that's what you want to do. Most people here start with the website rome2rio.com and you can put in your start and end destinations and get suggested routes including buses, trains, taxis etc. The use of R2R always comes with a big grain of salt but it's a good place to start.
Itabus offers Siena train station to Rome train station buses multiple times a day taking about 3 hours and costing 5-10e a person.
https://www.itabus.it/en/
There are other bus companies as well so feel free to browse.
Personally back tracking on the train to get to the big city and take the faster trains isn't a big deal but if the bus works for you it looks like a cheap and time effective option.
Have a great trip,
=Tod