Is Sunday a bad day for bus travel in the hill towns?
The buses run less frequently and on some routs not at all. Assisi to Firenze by train, then bus from Firenze to Siena is your best bet.
There is only one daily direct bus between S. Maria degli Angeli (down the hill from Assisi) and Siena: http://autolinee.baltour.it/Home/455-1-en.html.