The Titsa bus service offers a reliable public transport service all over Tenerife. I highly recommend getting out of the resort areas & exploring the rest of Tenerife.
The only buses I've found not to be all that reliable are the 103 and 110... usually replaced by the regular "all stations" 102 & 111 services, respectively.
Bus trips in Tenerife are
relatively expensive, but you can save a lot of money by buying a BONO bus card. They're available from all major bus stations & some newsagents. Just say: "Un bono, por favor".
They look like this:
The cost of a single journey between Playa de la Americas & Puerto de la Cruz (the longest bus service in Tenerife) will cost €12.25 if you pay in cash. If you have a bono, the same bus trip 'only' costs €7.25. Most shorter journeys cost €1-2 with a bono bus ticket. Bono bus cards cost either €12 or €30, so it's often worth buying one. I see tourists get ripped off all the time...
See this thread
for more information about travelling with bikes on buses.