score:5
Did you look at taking the train? Most of the places you mentioned are covered by the Spanish rail network. If you book in advance, prices are pretty good. For example, Madrid to Malaga starts from only €35 (advanced purchase, single train).
For some general advice on travelling by train in Spain, the routes etc, see the Seat61.com Spain page. For exact timetables, routes, and to book tickets, you'll want Renfe.com.
Upvote:2
I wouldn't go by bus, at least from Madrid to Sevilla, so boring. Instead i would go by ave (high speed train) that is more expensive but as they said above, if booked in advance the ticket could be cheaper than the bus.
Upvote:7
What is the cheapest (yet still reasonably comfortable) method to travel between these Spanish cities?
As you asked for the cheapest way, in my experience that would be the bus; those are generally cheaper than trains in Spain. (What surprised me is that on some routes the bus is also faster than train.) Connections are frequent and the buses are generally very comfortable.
Granted, it was back in 2005 when I travelled more in Spain (including Andalusia), but I suppose the situation hasn't changed too much.
The train answer mentioned Madrid to Málaga as an example (cheapest fare 35 € when booked in advance). On ALSA, the trip costs 23-24 € (no advance booking required). As another example, 8 hrs night bus from Cádiz to Madrid is just 25 € with Socibus.
Photo credit: http://autocaresdemadrid.blogspot.com/
There are several bus companies (partial list) operating in southern Spain. I don't know if there's one website to see all timetables though. What I did was simply go to the bus station in each city or town, check timetables there & buy the ticket; this worked fine. (Or google e.g. "sevilla cadiz bus" to find relevant company website with timetables.)
Btw, while you're in Andalusia, I'd recommend Cádiz, on the Costa de la Luz, less than 2-hour (12.20 €) bus trip from Seville (though not exactly on your planned route).