I need Information to travel by Bus from Algarve, Potugal to Seville, Spain
Absent knowing where in the Algarve, leaving from Albufeira, the ALSA bus would take about three hours. Alsa.es is the web site.
I was able to buy tickets in advance on Alsa through paypal in 2013. It save about 50% with the advance purchase from Coimbra to Salamanca. A little advice-- if you do not speak Portuguese write out in advance in any questions you may have at the bus station. We had a few tense moments at the bus station finding the Alsa bus for Spain but all worked out well.
In Rick's books, this bus trip is summarized on pp. 731-2 in Spain and pp.145 & 167 in Portugal (generally the start and/or end of each relevant chapter).