We will be traveling from Madrid to Granada and then Seville. Would you advise we rent a car or take the bus?

How about the AVA , Madrid-Seville, then Seville Cordoba, a quick visit in Cordoba and then a bus to Granada. How does this sound to you?
The AVA is fast and efficient, Tourist class is more than enough. Actually is very good.

We have to end in Seville because we are flying out of there

I did this trip last week. Took the AVE Madrid to Cordoba (less than 2 hours, 54 euros). Spent plenty of time in Cordoba to see the Mezquita and have lunch, walk around the Juderia, then bus at 4.30 (11 euros) to Granada. Arrived around 7pm. Very easy indeed.

Sorry, meant to add I then went by train to Seville, 3 hours, 17 euros. Comfortable, efficient. I didn't book anything in advance, just bought tickets on the day at the various train and bus stations.

I think Gertie 's combination is great.
If I understand correctly, AVE from Madrid to Cordoba, then bus to Granada, then bus to Seville, or did you do bus back to Cordoba and then AVA to Seville?
Either way seems perfect to me.

Sorry, or did you take a regular train between Granada and Seville, for 17 euros ? I got a little lost...

We toured that whole area by car and found it to give us a lot more freedom as to what to do when, where to stop, where to eat, where to explore, etc. But then we almost always do road trips - since we both enjoy the driving as well as the freedom it provides.

Yes, what I did was Madrid-Cordoba-Granada-Seville.
Stayed overnight in Granada for 3 nights then on to Seville for 3 more nights.

Hi gertie's itineray makes a lot of sense to me. To tour by car is of course very nice, but in your case, you do not need a car neither in Madrid nor Seville, that leaves you how many days to rent a car? Less than seven days does not make too much sense, also you would have to pay parking in Cordoba, if you go, and Granada,...

I would fly from Madrid to Malaga, pick up a rental car there and drive the approximately 82 miles to Granada(per www.viamichelin.com), in about an hour and a half. I find an $87 one-way plane far on Spanair by using a flight search in www.sidestep.com.

We LOVED driving from Sevilla to Granada! Roads are two lanes, but wonderful, driving is easy, and the scenery is simply spectacular!

I think our hotel in Granada charged us $12 per night for garaging our car in Granada. (We stayed at Hotel Inglaterra and liked it fine.)