What is the best way to travel from Madrid to Cordoba--by train or by bus?
Train takes 1:45 and the bus ride is almost 5 hours. I would definitely go by rail.
AVE Train.
high speed AVE trains
http://www.raileurope-world.com/train/spanish-day-trains
airline style variable pricing so book in advance
I'd also suggest taking a high speed train ( AVE or ALVIA) from Madrid (Puerta de Atocha train station) to Córdoba.
You may book your tickets in advance for best savings on Renfe.com.
Enjoy your trip!