1) You need not start riding from the airport because the buses take bikes and you can go almost anywhere in Spain by bus.
2) forget camping. Campsites are rare in Spain: not many people do it. The weather is too hot in the summer and too cold in the winter, so campsites tend to cater for caravans and campervans, which offer escape and shelter from heat and cold. Hotels in the south are about €40 for a room that takes two people.
3) go for a menu del dia for €10 at lunch and buy a salad from a supermarket and bread, and eat that in the hotel room in the evening. Restaurants are shut until 9pm and you'll want to be asleep by then so you can get an early start before the heat of the day.
4) plan it on Google maps and email hotels one or two days before you turn up.
5) be careful - some large towns have no hotels of any kind. You can find yourself with a 30k unexpected ride at the end of the day to a hotel.
Good stuff, agree about buses, people say they don't take bikes, some company websites too, but in real life, they do. I can't agree with 5 though, in many Spanish tours (north, south, across) I've never not found a room (I know you said hotel) and I've never booked ahead. They might not be immediately obvious but even small villages have rooms, might be above bars or in homes, but it'd be highly unusual not to get a bed, outside of feria time anyway. I'd pay 25 euros tops, for 40 euros I'd want a 3* hotel with a buffet breakfast, then feast and snaffle enough food for the day making it just as economical.
A week is not long and it depends what you like, Extremadura is nothing like Catalonia.
Madrid - Bilbao (Santander) is a good trip and a loop around Catalonia inc Girona and the coast via BCN would also be good
