Tourists are wasting money, so here is the simplest explanation for how Funchal bus tickets work

RULE 1 : DON'T THROW AWAY THE TICKET CARD it's rechargeable and worth €0.50

Rule 2 : don't use bus for short journeys, cos 1 short/long time on each bus costs 1 credit.

from CITY CENTRE : DO NOT BUY A TICKET ON THE BUS, as there are generally no GIRO ticket machines in the suburbs. Ticket machines are mostly along city centre sea front (+ Anadia shopping & post offices). So buy a ticket from the GIRO machine/office 

and put at least 2 credits on your ticket, so you can get back to city centre.

from SUBURB : The first time if you don't have a ticket you must buy a GIRO magnetic ticket from the driver for €1.95, including a 50c charge for the card. When you reach the centre, recharge your ticket at a machine.

RECHARGE OPTIONS : €1.35 per journey (2014 prices)

or €1.25 if you add more than 10 credits.

- A separate €4.60 daycard is available, or 3 days €11.80, or 5, or 7 days.

* 1 ticket for each person

SHARE AFTER - Before you leave give your card to someone else to add credit to.

* ask office or driver for Funchal busmap - it's useful : online http://www.horariosdofunchal.pt/index...

- On the back it lists the GIRO ticket recharge points.

* also get a Whole Island bus map from the tourist office : online : http://madeirarural.com/blog/tag/bus-...

CHECK YOUR BUS TIME : http://www.horariosdofunchal.pt/mobil...

OUTSIDE CITY - On journeys out of Funchal on the same company they charge you 2 or 3 credits. But most regional bus are operated by companies who charge you on board.

for Funchal : YELLOW bus website has all the info : http://www.horariosdofunchal.pt/

...

from 2010 You may see references to a "weekly tourist bus ticket" around the area. Do some research before you purchase these tickets (16 Euros each, more now)  - they are valid only on Horarios do Funchal buses operating within Funchal and a couple of nearby villages. They are not valid on Rodeste or SAM buses, and they don't even work on Horarios do Funchal buses going to comparatively close places like Camacha.

As Funchal is small enough to walk everywhere, you may not need a ticket like this - it could be cheaper to purchase HdF bus tickets on the vehicles themselves when you needed them.

That said, all the buses are cheap and reliable, and the scenery makes every ride memorable.

Buying bus tickets

Tickets for the city buses - "Giro" - can be bought on the bus, in several vending machines along the Avenida do Mar or at the Horarios do Funchal office in the Anadia Shopping centre. The physical ticket itself costs 50cent and each journey 1.35 euro. If the ticket is bought on the bus, the journey costs 1,95 euros. 

Once in possesion of a physical ticket, it can be recharged in the vending machines, the Horarios office and in several shops in the city center, including Bazar do Povo and the tabacaria in the Sao Lourenco shopping center (where the hotel buses stop). 

The bus to Monte 

Going by bus to Monte is quite an experience, just as much fun as the funicular, at a fraction of the price ! From the city center there are several bus lines to Monte, and line 48 goes to Monte from the Est. Monumental/ Lido area.

The bus to Ribeiro Brava

This is a great ride along the coast from Funchal on the No 7 Rodeste bus. It takes about an hour, going up and down and round the wiggly roads, and is great value at €2.70. You can return via the expressway in half the time.

Airport Bus. (Aerobus) is very cheap but can be unreliable. No timetables at Bus Stops outside of the centre and could run up to 1 hour late to the Airport.