Upvote:5
Tenerife has a bus system (TITSA) with an English-language website, which includes a tourist-oriented section. Depending on how many people are carrying the four bags, and their sizes, this may or may not be viable.
To get between Tenerife Airport North (Los Rodeos) and the ferry port (Estación Marítima), you will need to take Route 20 from the airport to Intercambiador Santa Cruz (Santa Cruz Exchange), the end of that line. You'll then need to transfer to one of Lines 910, 945, 946, or 947 to get to Estación Marítima (two stops.) Line 20 runs at 15–25 minute intervals from about 5 AM to 1 AM on weekdays, slightly less frequently on weekends and holidays. The ride is approximately 20 minutes from the airport to the Exchange.
To get between Tenerife Airport South (Reina Sofia) and the ferry port, take Route 111 to Intercambiador Santa Cruz, and then proceed to the ferry terminal as above. Service on this line operates 24 hours a day, with departures approximately every half-hour. The duration of the trip is unclear from the timetable, but it's 1h05m in the opposite direction.