Jennifer, we also used ALSA bus to go from Cordoba to Granada, and then from Granada to Malaga, and I highly recommend the bus. It is modern, comfortable, and air-conditioned. There are plenty of taxis waiting outside the bus station in Granada. You can also take ALSA bus from Granada to Cordoba.
We loved the Alhambra! It is magnificent and outstanding, and one of the highlights of our travels. We spent all day there. Our timed entry ticket to the Nasrid Palace was for 9 or 9;30am, and we arrived about 30 minutes early. We took our time in the Nasrid Palace, enjoying the ambience, and taking photos. We had lunch on the grounds sitting on a bench (we brought sandwiches). Then we slowly walked to the Generalife Gardens, and took our time there. On our walk back to the Alcazaba, we stopped at the Hotel America for drinks and snacks, so we didn't leave the Alhambra until around 4:30pm. The Alhambra is not a place to rush through. We also took the evening tour, which I recommend. It is less crowded, peaceful, and beautiful, and you can hear the water flowing and bubbling. The lights highlight the intricate carvings and tile work on the walls and ceilings.
We really like Granada. Architecturally, it is very different from Seville and Cordoba. We stayed 2 nights, but I wish we had 3 nights. I agree with the poster who said the bottom of the Albaycin is touristy with lots of tourist shops. I wish we had the time to wander through the upper part, which is why a 3rd night would have been nice.
We also loved Cordoba! it was one of our favorite cities on our trip during September 2017, and it is much less crowded than Granada and Seville.
You will have a wonderful trip!