It is a bit confusing to book a bus from Seville to Granada over the web (from Chicago, IL, US). The site I have tried to use is gospain.about.com. There are two bus stations in Seville. The site says the one servicing Granada leaves from Prado de San Sebastián, however, the ticket sale site only gives choices for buses that leave Plaza de las Armas. Which is correct? And if someone knows is this the correct site for booking these round trip tickets? Thanks in advance.
Try ALSA.es. That is the bus company. It shows the Granada buses departing from Plaza de Armas. You can also take the train; it is pleasant and comfortable.
I don't believe there is any discount for early purchase so there is really no need to buy tickets in advance. When we have used the buses in Spain we have always bought the tickets just before departure.
Frank is right, no need to book the bus ahead. They leave about once an hour so there are plenty. If you decide to take the train, book that a day or two ahead as the train runs less often and does fill up.
According to the ALSA website under "offers", there is a 25% discount for advance purchase (15 day) on some routes, but not Sevilla to Granada. If you are using other buses you might check it out.
Thanks to all, we are going to take a look at that website. Looking forward to this trip!
Assuming you are going to Granada to see the Alhambra, it is a good idea to book your tickets in advance. They do sell out-we saw lots of disappointed people on the mornings we were there. In addition to the regular visits to the palaces, gardens and fort, all included in the "general day visit", you might consider one of the walking tours, called "Visitas por el entorno urbano and paisajistico". http://www.alhambra-patronato.es/index.php/Tour-of-the-Landscape-and-Urban-Environment/191+M5d637b1e38d/0/ These are themed walks, different on different days of the week, and include some area that are not open to the general public. We did the "Conquest of Water" tour on a Thursday and it was fascinating. Note that these walking tours do NOT include entry into the Nazrid palaces on your own; you may only visit certain areas with the guide. These tours are not a substitute for the "general visit" but a supplement to really learing about the Alhambra. Our tour was about 5 hours.