If you're flying into Madrid and want to go directly to Granada, why not just book your ticket to Granada as your final destination. Depending on who you're flying with, the add on isn't that much. Talk to an agent (airline or travel agent).

If not, then taking the train will be difficult. There are normally only two trains/day from Madrid to Granada, one in the early morning, the other in the late afternoon. They take around 4-1/2 hours to make the trip, and the tickets (Preferente) are not inexpensive.

The ALSA bus takes anywhere from 4-1/2 to 5-1/2 hours, with several departures a day. There is one from the airport, but it only has limited departures.

I took the bus from Granada to Madrid, after having taken the AVE to Sevilla and then bus from Sevilla to Granada.

Is the bus the best way? It's probably no worse, as I think the train would have gone to Sevilla or Granada before cutting over to Granada. And it wasn't cheaper.

Only thing to be wary of is that the bus station in Granada is a fair distance from the center of town (cathedral) and the Albaicin.

But there is a bus that goes direct from the bus station to the center of town. Obviously taxis as well.