TG Comes also run buses four times a day between Algeciras and Seville, takes 4 hours.

http://www.tgcomes.es/horarios_33.htm

There is no practicable route by train.

Am fairly sure that you need to walk up to San Bernardo main bus station at Algeciras where you have the choice of either the LINESUR or COMES service. The LINESUR one goes up the good dual carriageway road from Los Barrios to Jerez then continues up the main motorway so is a nice journey in my opinion. Although a few of these bus do make additional calls. Look at the timings on :

activagest.com/linesur/…algeciras.pdf

The bus station is at the following address which can be used on Google Maps:

Calle San Bernardo, 1, 11207 Algeciras, Cádiz, Spain

about 15 - 20 minutes walk from the ferry terminal