There are several possibilities to travel from Cadiz to Tarifa or visa versa. One of the easiest ways is to rent a car. There are a couple of car rentals in Cadiz:
Another easy way is to go by bus. The bus to Tarifa leaves from the ‘estacion de autobuses’ in Cadiz. The bus to Tarifa leaves six times a day. The Cadiz-Tarifa bus leaves also six times a day. The price for a single ticket is around 9 euro per person. You can buy the tickets online or at the bus station.
See for the exact timetables:
Also check these sites:
TIP: Be careful! Always check the timetables to plan your trip, they are constantly changing!