The bus is a good option to get from Siena to Florence. I think you are confusing the situation with the location of the bus station however. It's the bus station in Siena which is in a much more convenient location the train station. You can get the bus to Florence at Piazza Gramsci in Siena - a short walk from the historical center. If you take the train, you have to take a city bus or walk from Piazza Gramsci down to the train station. You can buy tickets at the Piazza.
The buses run frequently - I recommend an express bus that only has a couple of stops between the two cities. Once in Florence, you are dropped off at the bus station which is just around the corner from the main train station and a short walk to the main tourist sites.
The bus is run by the SITA bus company This might help (But might also be out of date)
http://www.discovertuscany.com/attachments/SITA_Firenze-Siena.pdf