Train or bus?

The bus is a little slower than the train but offers more schedule options. For such a long trip, I recommend a train so that you can be more comfy and walk around. This is not on the high-speed AVE train line, but it still gives you more room than a bus does.

The bus station in Madrid is next door to the train station.

Yes the bus station is right next door to Atocha station, which is where you would arrive by train. If you're packing light, you can catch a metro to whereever your hotel is located (if it's not walking distance). If you have luggage, you will probably want a taxi. The busses are nice - essentially new charter busses - so plenty comfortable. The trip by either takes about the same amount of time, the busses go straight there while the train takes a more circular route. The busses are way cheaper than the train - especially if you don't purchase your train ticket well in advance - and you can usually walk up without a reservation (I like to purchase my ticket the previous day to be safe).

Which bus station are you talking about? The bus from Granada arrives at Estacion Sur, which is not right next to Atocha but a metro ride away. If you buy train tickets in advance you can get the Web fare which is not much more than the bus fare. Edit: no Web fares left for Oct. 19 but there is an Estrella fare of 41 euro for the evening train.