The main bus station at Algeciras is called San Bernardo and is situated opposite the railway station. There are normally taxis outside for onward local travel and it is about a 20 minutes walk mostly down hill to the port departures/arrival terminal building where you can take a ferry over to Tanger-Med or Ceuta.

The local bus infornmation can be disovered using this link

and on the main page which is in Spanish you can open Lineas y Horararios to obtain the routes and times. For example a bus round the bay to La Linea de la Concepcion for visiting Gibraltar can be found as route M-120 or M-120D (for direct) 

Or the bus to Tarifa in the other direction is listed as M-150 

Long distance buses call in here. For example those from Cadiz to Malaga. Or from Algeciras to Jerez or Seville.  

The bus station has a cafeteria if waiting and also some lockers. A small shop sells the usual things and toilets are adjacent. 

Algeciras bus station