The route you are taking -heading south from Madrid- is not very pleasant, at least the first 80-100 km. approx: southern Madrid is ugly, just big suburbs and industrial areas, lot of highways. I suggest you take a train - Regionales - to Aranjuez for example. It will be a nice starting point for your bike route.
In sothern Spain it will be difficult you find any hostel, but I think you will not have any problem finding small hotels, hostales even in small villages. In non touristy areas prices are good, I paid 18.00 euros for a room one week ago in a nice small village hotel in the interior.
If you plan to camp please avoid to make any fire in the country, fires are a big problem in Spain and not only in the summer.
Feel free to contact me if you need additional info.