Public transport??
Bus to Jerez.
Bus from Jerez to Algeciras.
Bus from Algeciras to La Linea.
Five minute walk across the frontier.Â
No idea how long the trip from Jerez to Alg takes, prob 2 or 3 hours.
Forty minutes or so from Alg to La Linea.
Linesur looks like the bus company to check out. runs a route between Seville and Algeciras via Jerez.
Hope that helps.