
Public Transportation in Madeira Island
Check the buses and their websites for more information:

Buses photo Credits to Horários do Funchal: www.horariosdofunchal.pt
What are the best options to travel around Madeira Island, Car-Rental or Public Transportation?
Public transportation is limited around the island and it will not take you to all locations in Madeira. Some locations you will need to hire a car, book a taxi service or arrange transportation with a local travel company. The time table for the north of the island is quite restrict and you may have to wait more than 1 hour for the next bus, while in Funchal city or in the rest of the south of the island you will have much more availability. The reason being is that more less 85% of the population lives in the South of the island with the biggest concentration in Funchal and on the north only around 15% of the population lives there. Also to purchase bus tickets can be confusing as you have different companies covering the island so you need to know which company you need to purchase the tickets. If you are staying in a hotel outside Funchal, most of the receptions can provide you with information of the buses you can take, most of them even have the time tables and fee guide.
In total you will find around 4 different companies, each of them will cover a different part of the island and all of them will depart from Funchal City.
Local Car Rental
Don't be stuck with schedules go where you want when you want.
There are a few local car rentals in Madeira Island, only the big international car rentals are located at the airport but if you request a local company to bring the car to the airport they will do that for a small fee or without a fee depending where they are based.

The ones I have use in the past with family and friends and I had a good experience with are:
Happy car madeira - https://happycarmadeira.pt/
10% off when you use this code WELOVEMADEIRA
WhatsApp: +351 914 673 372 - Bruno Teixeira
Espaço Milénio Rent-a-Car - https://espacomilenio.com/
WhatsApp: +351 969 103 199 - Ruben Costa
Rent a Car Tamariz - https://www.rentacartamariz.com/
WhatsApp: +351 918 221 057 - Hugo Sá
I find it easier speaking with them directly as their websites sometimes have some bugs and does not show the information correctly. They speak well English / Portuguese and they are very friendly and flexible. It worth getting a quote from them and compare prices.
WELOVEMADEIRA

Private Service
If you are looking to have private transfers from and to the airport or even organized day tours, Levada Walks and much more, I recommend this agency ALEXGO TRAVEL.
I have used them for tours with family and friends and also for private transfers to and from the airport. They are very punctual and professional.
They have more than 20 years of experience and they are the number 1 company to go to when you travel to Madeira Island.