Many people find no reason to use a car while in Andalusia -- it really depends on your itinerary. In many places, a car will actually be an impediment....

@palenQ I did find that train on oui.sncf, but the fare is somewhat higher. We were in Barcelona last year, or stopping there would be a great idea. But as the date is closer and flights are scheduled we will check our options to fly to Marseilles or train to Avignon. Thanks so much for your help.

Was just in Andalusia earlier this month. Took the ALSA bus from Granada to Seville, and it was an easy and comfortable 3-hour trip. Note that the prices vary considerably based upon the time of day that you are going. We took a noon - 3 PM bus, and price was well in excess of others during the day, and quite a bit more than a Madrid - Granada, 4 1/2 hour trip we took a week earlier.
One recommendation - try to avoid seats near the bathroom. We were seated directly in front of it on the Madrid - Granada bus, and the stink was overwhelming for the last 1 1/2 hrs or so.

This is what we did except we stayed in Madrid first, flew to Granada, rented a car, visited Cordoba and dropped off car in Seville. Flew out of Seville to Madrid to US.

Do you need to buy ALSA bus tickets in advance?

You can buy tickets right at the station, but if you have a pretty set idea on the times you will be travelling, I'd recommend buying them in advance. I don't know if this is normally the case, but on both of the trips we took, the buses appeared to be completely full.

It's easy to buy tickets on line, and you normally don't need printed copies ... you can use the emailed version with QR code, and they will scan them directly from your phone. The exception applies to international trips - my daughter and son-in-law took a bus from Seville to Faro, Portugal, and needed printed tickets for that trip.

https://www.alsa.com/en/web/bus/home

We had a great time and, indeed, flying to Granada worked out perfectly. Thanks to everyone for your help! Here's a link to my TR:
TR: Andalusia and Madrid May 2019 (LONG)