I spent many summers in the area just to the west of Bolsena. The Via Cassia (SS2) can be narrow busy and fast in that area. No shoulders. Despite this, there are always tourists riding on the side of the road. But I would avoid it and do the western route. And it is hilly. All the small towns have some sort of restaurant or small (sometimes very small) hotel. You can then get back to the Cassia if you want at Acquapedente where the riding is more reasonable. There is a mile long tunnel after the first turnoff for Radicofani. Have bright red blinking tail lights! Or if you're adventurous enough, ride up the mountain to Radicofani and enjoy the view. There is another road back down to the Cassia on the other side of the tunnel.

Just know that the Via Auralia (A12?) on the coast is a superhighway from Fiumicino to Civatavecchia and probably not bikable. After that it isn't a great road to ride on either. There are routes through the hills and back country, but you'll have to plan well.

It sounds like a great adventure and I wish you well!