I studied and lived in Granada (capital) last year at 19, and made the Madrid-Granada treck many times. Your two best options, like was mentioned before, are the bus, or the plane. Ive done both, so here are my thoughts:
-Bus: From the airport in Madrid, she would need to get to the bus station, and catch a bus from there down to the town where she will be staying. Madrid-Granada (the city), is around 4-6 hours if I remember correctly. Cheap, and buses are pretty comfortable. As far as getting to the bus station, you can take the metro, but with lots of luggage to weigh you down, a taxi may be a better option. One thing to think about, the flight to Madrid from Cal is a really long haul, and so the idea of sitting on a long bus ride, waiting around in a bus station, etc, may not be so wonderful at that point.
-Plane: I flew the Iberia Madrid-Granada route a couple times. It saves you the trouble of leaving the airport, dealing with finding a bus ticket, the metro, taxis and what not. Its about an hour long flight, and I think there are a couple daily. Lots of times you can get really good deals also through Iberia, especially if you are attaching it to a transatlantic flight with iberia. check out
www.iberia.es and look for deals. In my personal opinion, if it was me, Id get a flight down to Granada, especially for a first time solo traveler in spain. Although it may cost a little more, itd be worth it to me.
Just my opinion.
Good Luck!
Kelly