Does anyone know if there is a bus from Tarifa to Cadiz that runs regular weekdays?
Yes, there typically are several a day. Both Avanza https://www.avanzabus.com/ and Alsa https://www.alsa.com/en/web/bus/home run that route direct. Trip takes just under two hours.
We took that bus Paul is mentioning in February 2024. Yes, it’s multiple times per day. We stopped on the way from Estepona to Cadiz and ate lunch at Tarifa. I loved Cadiz! Have a gelato or two at this shop for me. It’s in the Top 5 I’ve had in Europe: