Probably, there are locals out there on Tripadvisor that might have better knowledge,
but, I was researching something similar about 15 months ago.
If you want to use public transport; there's a travel planner here:
You'll find, that you need to take a bus to Granada, then change to a local bus
to Capileira, and it takes 4 - 6 hours.
Some of the buses depart from Malaga Aeropuerto, although it is not possible
to search for this on the travel planner. If not, you'll need to take a local bus
to the Malaga bus station.
The long distance bus is frequent, efficient and comfortable.
The local bus is not so frequent, meaning that there will be some waiting time.
The journey is spectacular.
The travel planner cannot handle any date longer away than a month or so,
but if I understand things correctly, the timetables are fairly stable.