From the Costa del Sol the tourist buses leave very early to go to Granada for the Alhambra. They start at about 6am and pick-up all along the coast before heading to Granada at about 8.30. So if you are at the start of the run you sit on a coach for about 4 hours before reaching Granada.
We now recommend to our guests that they drive to Granada but book a "Bono Touristico" ticket before they come to Spain which includes entrance to the Alhambra and Generalife, the Cathedral, the Royal Chapel, the Monastery of Cartuja, the Monastery of San Jerónimo and the Science Park. It also includes 9 free journeys on normal buses and minibuses, and 1 free day on the CITY SIGHTSEEING bus.
There are details on the granadinfo.com website. You pick up your tickets in Granada at Plaza Nueva and you have the whole day to enjoy Granada.

Thanks for that..........I'll start investigating!

Hi there, we are visiting Nerja for the first time at the end of the month and I've just booked our Alhambra tickets. If you do decide to drive and need to book your tickets independantly then I found this "how to" link extremely helpful - http://www.tripadvisor.com/ShowTopic-g187441-i416-k2209992-Booking_Alhambra_Tickets_Through_Servicaixa_Revised_Aug_26-Granada_Granada_Province_Andalusia.html
It does say you don't get an email confirmation and to print the booking page but actually there's a box you need to tick and we got ours OK.

There's a tourist information point on the Balcon de Europa in Nerja and I've been told they can help with all trips etc. You can email them here - turismo@nerja.org

Thanks Puddleduck: I'll check those out.
Have a great holiday & if you've any useful info please post & let us know how you get on as we're going at Hallowe'en/

Will do, I'll be doing a trip report when I get back anyway so look out for it.