Unfortunately, there is no direct bus service between Faro Airport, Faro, and Marbella.
However, all buses between the Algarve and Spain have to transit via Sevilla.
Consequently, you should be able to get a bus from Faro Bus Station to Sevilla Plaza das Armas Bus Station, take a local Tussam C4 bus to Sevilla Est. Prado Bus Station and then another bus from there to Marbella.
From Faro Bus Station there are departures daily to Sevilla Estacion Plaza das Armas Bus Station by DAMAS/EVA TRANSPORTES ( http://www.eva-bus.com/ ) as follows:
0740 (summer only - 2014 to be confirmed) arrive: 1130
0820 (year round) arrive: 1300
1355 (summer only - 2014 to be confirmed) arrive: 1745
1535 (year round) arrive: 2015
From Faro Bus Station there are departures daily to Sevilla Estacion Plaza das Armas Bus Station by Alsa.es as follows:
01:45 arrive 05:45 (This bus also continues to Est. Plaza das Armas Bus Station )
This service does offer a connection onwards to Malaga and then Marbella BUT it is a circuitous roundabout route!
There are three departures per day from Sevilla Est. Prado Bus Station to Marbella.
The Bus Company is AUTOBÚS DE LOS AMARILLOS.
The link for the timetable is here:
http://goo.gl/AD4DV
There are daily departures to Marbella from Sevilla Est. Prado Bus Station at:
10:00
15:30
18:00
Transit time is 3hrs 30 minutes
Bear in mind, that Spain is on Central European Time and is an hour ahead of Portugal.
All times shown above are based on local time.
In summary, therefore, it would appear that the 08:20 DAMAS/EVA bus from Faro to Seville Est. Plaza das Armas, and the 15:30 from Sevilla Est. Prado Bus Station would offer the best connection.
Be aware that in busy periods buses may be busy.
Go to www.eva-bus.com for the Faro to Sevilla Segment. It does not appear possible to purchase the tickets from Sevilla to Marbella on-line.