Tenerife South is the biggest airport in the Canary Islands, and Teide is them most popular tourist attraction, so it would be very useful if the internet had information to offer as to how to get between the two. But Wikitravel, Tripadvisor and Lonely Planet Online don't say anything, and neither do the blogs I've found.
Google Maps suggests Bus 111 and then Bus 342 (2 hours, 25 minutes), but for each day the only route it gives begins at 8:30am. I find it hard to believe there's only one bus going there per day. I'll be arriving at around 3pm at the airport, so I need a later bus or shuttle.