The bus system is quite complicated in Madeira. They are now officially all one company but they still go from separate places and only Horarios de Funchal are on Google Map. For future reference for anyone visiting the best buses to take for hiking/exploring are....
SAM 113 to Bahia d'Abra after Caniçal for Ponta de São Lourenço hike (you may well see it from the plane). Don't miss Prainha beach near there, down a slope before São Lourenço peninsula, it's fantastic and natural sand. The hike there is totally different to the levadas or any other walk on the island.
SAM 103 maybe others to Ribeiro Frio, which is a nice place. Great for Levada dos Balcões or Levada do Furrado to Portela. Buses back from Portela too.
Rodoeste various to Ponta do Sol (for Rodoeste try and get express buses the normal ones are very slow) then walk/taxi/local bus for the circular Levada Nova Levda do Moinho circular hikes from Igreja da Lombada.
Horários de Funchal 81 to Curral das Freiras then walk up to Eira do Serrado. Or go up there first, some buses go up to the viewpoint. then walk down. Great views. Lots of nice snacks made with chestnuts (castanha) in Curral das Freiras.
Horarios de Funchal 20, 21, 22 (maybe others) or the Teleférico Cable Car to get up to Monte for the palace gardens and the walk along to the botanical gardens if you're feeling adventurous. Then you can walk down or get bus or the Teleférico down from the botanical gardens even (not cheap but great views).
Pico Arieiro for the AMAZING Pico Ariero to Pico Ruivo PR1 walk. Highly recommended. Horários de Funchal from the Teleférico at 6am and 1.30pm only. Both sunrise and sunset are great there, weather permitting. Most people drive but you don't have to. Very easy to hitchike back with tourists too, Germans/French/Poles/Czechs much more likely to pick you up than locals.
SAM various buses regularly to Machico, then hike Pico do Facho to Caniçal, then bus back from there to Funchal. Both nice towns. Caniçal has a whaling museum too and some nice wilder swim spots when weather is better.
Horários de Funchal local bus lines 1 and 2 and 24 to Praia Formosa on the edge of Funchal. You can then walk back along the sea front from there though a tunnel then to Lido and back into town that way. Or you can follow the sea walkway all the way to Câmara de Lobos along the beach (been closed recently but usually open) and get Rodoeste bus back from there.
And finally one for the intrepid. Rodoeste to Corrida on the slow bus then walk up a steep road to Boca da Corrida. Amazing viewpoint. Great great hikes from there include hike to Boca da Encumeada in the centre of the island (some buses pass by there but not many). Hike to Curral das Freiras which can be combined with an ascent of Pico Grande if the weather is clear. It's quite hard. One of the best hikes ive done though. You can then get bus back from Curral das Freiras.