What's the cheapest option other than flying?
nothing: Walking down to Naviera Armas. I estimate that took half an hour, including detours due to construction work. By the way, Fred Olsen is next to Naviera Armas. Hint: In the port, follow the blue line!
14 EUR: Ticket for the ferry from Santa Cruz de Tenerife to Las Palmas de Gran Canaria, bought at the office on location. The ship took something like 2.5h. About the low price: Someone told me that Naviera Armas is heavily subsidized by the EU. In the ferry there is free Wi-Fi and free electricity. Also there are several sun decks, there is a bar, and they show a movie. It's very spacious. Don't expect luxury, though.
nothing: Bus transfer from inside of the Port of Las Palmas to the city. This took maybe five minutes. From the spot where the bus dropped us off, my accommodation (Airbnb) was perhaps 300m away.
That was off-season. On March 29th 2013, Easter holidays, I traveled in the opposite direction. This time Naviera Armas would have cost 35,20 EUR, and interestingly Fred Olsen had a much lower price than before: 35 EUR. Possibly they were running ferries at a higher frequency. Naturally, I chose Fred Olsen: free bus transfer from Las Palmas to Agaete (1h), then ferry (1h)
Notes concerning Fred Olsen:
If you buy the ticket from Fred Olsen online, then the printout is not sufficient for boarding. You have to go to a Fred Olsen ticket office, e.g. in Agaete at the port, show the printout, and then you get a boarding card.
While the boat didn't have a sun deck, in the back there was an area open to the outside, where people were smoking or just enjoying the view.
You can take the ferry with Fred Olsen. There should be buses from Tenerife South Airport to Santa Cruz de Tenerife. From the main bus station, there are then dedicated buses to the ferry terminal, from where there are several ferries per day to Gran Canaria. The bus from the intercambiador (bus station) to the ferry terminal (a short ride) is included in your ferry ticket.
I made the journey from Gran Canaria to La Palma, via Tenerife, last December. I have written a mini-travel report in this answer. Your journey will be:
- Airport bus from Tenerife South Airport to Santa Cruz de Tenerife (note: I did not check how this works, I simply assume there is one). Please verify that this one indeed gets you to the intercambiador.
- Ferry-bus from Santa Cruz de Tenerife Intercambiador to the ferry-harbour. This is included in your ferry ticket.
- Ferry from Santa Cruz de Tenerife to Agaete on Gran Canaria
- Ferry-bus from Agaete to Las Palmas de Gran Canaria. The bus departs from right outside the ferry. To be sure you might want to ask; I took it in the other direction. The bus is included in the ferry ticket. This bus takes you to the office of Fred Olsen in Las Palmas, from where it's a short walk to the Santa Catalina bus station.