The answer
Take TITSA line 40 from the stop opposite arrivals — €3.20 to Los Cristianos and €3.70 to Costa Adeje paid in cash or by contactless card, dropping to €2.80 and €2.90 with a Ten+ card, roughly every 30 minutes.
The south resorts are one straight corridor from the airport, the 40 runs it all day, and a €2 Ten+ card pays for itself on the first journey.
Heading to the capital? Line 10 runs direct to Santa Cruz for €9.35, or €8.45 loaded on a Ten+ wallet.
Landing after midnight? The 711 night bus leaves for Los Cristianos and Costa Adeje nine times between 23:00 and 04:50.
⚠️ The traps (walk past these)
Line 111 no longer stops at the airport
The 111 was rerouted and now only calls at the Enlace Aeropuerto stop on the motorway, about 2 km from the terminal — with no pavement and no way to walk in. Guides that still send you to the airport on the 111 are describing the old route.
Do this: take line 40 (or 343 or 711) from the stop opposite arrivals, and never plan to walk from Enlace Aeropuerto
Paying cash charges you the tourist rate
The same seat on line 40 is €3.70 in cash and €2.90 with a Ten+ card; to Los Cristianos it is €3.20 against €2.80. TITSA's whole pricing model rewards the card, and the gap widens on the long runs — Santa Cruz is €9.35 cash against €8.45 loaded.
Do this: buy a €2 Ten+ card at the airport ticket machine or use the Ten+ Móvil app before you board
The 343 takes twice as long as the airport claims
Aena's page says the 343 runs between the two airports non-stop in 50 minutes. TITSA's own page for the line gives 100 minutes. If you are connecting between Tenerife South and Tenerife North, the short figure will make you miss the connection.
Do this: plan on the operator's 100-minute figure and leave an hour and three quarters between the two airports
There is no tram, and nothing after the night bus
Metrotenerife's tram runs only between Santa Cruz and La Laguna and serves no airport. The 711 night bus is the only service in the small hours and it is not hourly — after it stops, the taxi rank is the only way out.
Do this: check the 711 times before relying on a late landing, and fall back on the taxi rank if it has gone
A travelcard is not the cheapest way to make one trip
The 24-hour travelcard is €10 and the 7-day pass €50, and both are personal — one per person. For a single airport run, or for two people, loading the shared Ten+ wallet instead gives the same discounted fares without paying for unlimited travel you will not use.
Do this: buy a €2 Ten+ card and load the wallet for airport runs; only buy a travelcard if you will ride four or more times a day