Bus from Madrid to Cordoba

Why the bus and not the train? When we use the bus in Spain we just buy the tickets prior to boarding. I am sure that there is no discount for early purchase so why do it?

You also might want to remove your email from your post. This is a forum helpline, not a direct line to Rick Steves himself. We are just volunteers from around the world helping people with European travel questions. RENFE is the Spanish rail service and their website has an English language tab. But be warned, many people have a hard time getting their American credit card accepted using the RENFE site. Someone else can chime in with the details of how to make it work. There are steep discounts for buying a rail ticket ahead of time. Discounts enough that it might be cheaper than the bus. And the bus will take much longer. And if you do decide to stick with the bus, tickets can be purchased the day of or a day in advance. There is no need to buy those in advance.

Go to tripadvisor for best forum instructions on using Renfe, or google it. Be patient and follow the instructions carefully. Take the AVE and second class ticket to save money. Wonderful experience.
Safe travels

We took a high speed train from Cordoba to Madrid - and booked well ahead for a very affordable ticket. If you don't want to book ahead, but still get a great deal, you can show up at the bus station in Madrid without a reservation. Each station I visited in Spain (didn't go into a Madrid bus station but was true in Cordoba) had an information booth with an English speaker to help you navigate their system. Spain has multiple competing bus lines, which makes it difficult to calculate your options from here. The competition keeps the bus quality high (like tour coaches) and prices low - unlike what most of us have come to expect with Greyhound.