transfershuelva.com used to operate a schedule service between Faro Airport and Huelva.
I have spoken to them and they say at present they are only operating such a service by reservation and for groups.
A hire car is not really an option unless you are returning it to Faro Airport. If this is an option, I recommend Luzcar, (http://www.luzcar.com).
I have dealt with them for years. Their prices are inclusive and they allow you to take cars into Spain as far as Seville.
As regards buses, you would need to take a local bus or taxi to Faro bus station and then one of the three daily services from Faro to Huelva.
Cubsur has all the timetables from the Algarve to Spain on his website:
http://thomasallen.home.sapo.pt/travel/001.htm
