There are no direct buses from Faro Airport to Vilamoura. One either has to take a taxi or a private airport transfer.
One can also take a bus from Faro Airport to Faro City Bus Station and from there get a bus to Vilamoura. However, frequencies are not that good.
Cubsur has the times for the above services on his excellent website here:
http://thomasallen.home.sapo.pt/travel/003.htm
For Faro to Vilamoura services see his site here:
http://thomasallen.home.sapo.pt/travel/002w.htm
