All else being equal -- and I don't know that it is! -- I prefer a train if the trip is long enough that I expect to want to walk around and a bus if the trip is shorter, because then I don't have to lift my suitcase onto the train (luggage is stored in an undercarriage on the buses I took in Spain, or at least, it has been on all the buses I've taken there). Maybe that will help you decide?

For schedules, you might check rome2rio.com -- but be sure to check through to the underlying links, as the main site is not sensitive to seasonal variation in schedules.

I have read that you can take a train with a transfer to a AVE in Malaga to get to Granada is that a good way to go?>

Can't see how it could be over direct Madrid-Granada train/bus combo - there is an AVE-bus combo to Grandada about 11:30 too according to www.bahn.de/en - German Railays schedule site for all European trains and to me very easy to use- https://reiseauskunft.bahn.de/bin/query.exe/en?ld=3989&country=GBR&protocol=httpsrt=1&OK#foc us

Since you'll already be at the airport, why not fly? Check the flights on Iberia. Depending on when you will be arriving, there are direct flights that take 1hr 15min for as low as $64USD.

The only way to get from Málaga to Granada is by bus, car, taxi or private transfer.

+1 to flying. We landed in Madrid at 8am and took the noon flight to Granada. You might have to take the airport shuttle to switch terminals but it's easily done. You do have to book early as certain flights during the day are popular and can get full months ahead, especially during peak travel time. Our plane was definitely full in February. At the time I booked our flights, the one-way fare was also very expensive for some reason (200 USD) so I booked a roundtrip for 90 USD and basically threw the return away ticket. Just something to keep in mind.

I don't really understand why you didn't just add this flight onto your itinerary and have a flight connection. Maybe that depends what airline you are using to get to MAD, Iberia is the only one that flies from MAD to Granada (really Air Nostrum). But the flight is cheap and quick, seems easiest to me. There's a flight at 12:20 pm.

Otherwise, you just put in the destinations to RENFE and it shows you the options. IF this date is far out, check with a closer date to be sure. I don't know why you would prefer a train to a bus since you have to transfer if you take the train (at Antequera) and of course you can't take the train from the airport as there isn't a train station there. So you have to go into Madrid to get either the train or bus anyway. ALSA buses leave from several stations but mostly from Sur.

The next train is not 6 hrs later from 9:30, not sure where you saw that. There is a train at 9:35 am and then at 2:35 pm. That's five hours. YOu get into Granada finally around 6:30 pm. You'd get there around 1:30-2 pm if you fly. You certainly have plenty of time to check your bags onto that flight if you arrive at 8 am. Too much time really but you aren't getting there quicker by train, obviously. buses are 10:30 am-3 pm or 11:30 am-4 pm. Plus some later or earlier, of course.

I can't see why anyone would prefer that train if you are at the airport, I could see it if it were direct, but it's not. The bus station (Estacion Sur) isn't even that far from Atocha, although you can take some public transport to Atocha, that's true. Flying will cost more than the train or bus, but it's not an expensive ticket. I'd fly first, then take the bus. And if you just really prefer shorter time on a vehicle, the train option will be shorter actually on the vehicle than the bus. Depends what matters most to you, that or what time you arrive and how much time you waste.

Personally, I might have tried for a different flight schedule altogether, maybe going to Granada after some time in Madrid.

Yes flying makes total sense here - vs schlepping over to Atocha train station and then changing to bus and taking about 7 hours from airport.

I tried your roundtrip suggestion but the cost was about 180 Euros (checking a bag). One way was even more.
The train schedule is not great. Bus schedule is better and it seems to take about 5 hours from Estacion Sur. Certainly less expensive, around 60 Euros for three. Would you purchase a ticket ahead of time?
Also we plan to travel six days later to Barcelona from Malaga? Would you purchase that ticket ahead of time?

Thanks for all of the assistance.

Also we plan to travel six days later to Barcelona from Malaga? Would you purchase that ticket ahead of time?>

Bus or train - train yes for possible discounted tickets at Renfe - see www.seat61.com for superb tips on doing that -general info trains BETS-European Rail Experts and www.ricksteves.com.

There are direct trains Barcelona to Malaga that take 6 hrs and do not go thru Madrid - in fact nearly none of the connections between those cities go thru Madrid which would take much longer.

Yes I just checked www.bahn.de/en - German site which is usually right on and is in this case -but I only checked the first 3 trains of day which do not go via Madrid and not later which do go via Madrid. Presumably they would be on early trains, one at least direct. But in general most trains yes govia Atocha in Madrid and change there.

Yikes...why not fly? So easy.

Most people prefer Bus these days as there are delays with train travel due to engineering upgradation works going on which are due to complete by the first quarter of 2019. please confirm beforehand about train delays and if it has got back to normal then go for train travel.

Several times after scheduled re-opening of tracks to Malaga it has been delayed but has to open sometimes I guess.