been to Madeira 5 times, the first time we booked to take bikes but after checking the amount of climbing out of Funchal decided against it
I now just stick to walking (levadas and the 3 peaks route)
I did hire a MTB a couple of years ago, the locals all get the bus up to Poiso which is where the Arriero road turns off and take their bikes out of the luggage hold, driver is fine with this
From there it's an OK ride up to the summit then about 1/3 of the way back down is a tremendous singletrack route back to below Poiso where a hard grind back up to another MTB track of sorts which eventually brings you to the roads at the top of Funchal (essentially 90% of the inhabited area pf the whole island is on the slopes up from the city centre) from where it's a thundering downhill to the Beerhouse (brewery and tuna to die for!)
you can't ride along the levadas they are barely wide enough for 2 people to pass on foot with guard rails along all the hairy bits also lots of tunnels with a 18" wide walkway
Going back in a month, dirt cheap that time of year and still really warm
The climb to Pico Areiro from the north was sensational.
from Ribiero Frio?
even the bus struggles to find a low enough gear, but agree the view up to the Pico Ruivo etc is superb. If you only do one levada do the very short 1km one from Ribiero Frio to the balcony viewpoint, 100s of metres above the valley floor and 100s below the highest point.