Transportes La Palma (bus company)
Up to date timetable here
The website no longer has an English version or a map of bus routes, but they do link to a web or mobile app that will tell you which bus(es) go where you want, and when the next one leaves. They only offer Spanish, but I worked out how to tweak it into English. You’re welcome.
Timetable for Los Indianos 2017 HERE
Fast (2 hours) ferry to Los Cristianos in southern Tenerife
Naviera Armas ferries Slower and cheaper. There is no longer a direct ferry to El Hierro.
Ferries to S/C de Tenerife, Las Palmas de Gran Canaria, Lanzarote (Arecife), Fuertaventura and Cadiz
Binter Canarias Inter-island flights
Canaryfly Interisland flights (Fewer flights, but sometimes cheaper. No flights to La Gomera or El Hierro)
Thomson Fly Charter flights to London Gatwick and Manchester
EasyJet Charter fligts to London or Berlin
Iberia Spanish national Airline