Yes, there are buses but with traffic in the historical area, you might be able to walk there faster. Also, you need to know which ones to catch. Walks to the Accadamia and Uffizi are easy walks that take you past shops, squares, piazzas, etc. When walking from the Accadamis to the Uffizi, you will pass, or be within a block of the Bargello, il Duomo, the baptistery, the Duomo museum and other historical sites.
If you really must take the bus, the bus station is adjacent to the train station. They do have an information window where you can buy tickets but in our experience, they didn't speak English. However, I'm sure they understand "Accadamia" and "Uffizi".