For my travel I rented a bike from this rental shop.
Megasport Algarve rents a wide range of bikes, offers a bike delivery/collection service for free in the whole region, organizes also guided and self-guided tours of the Ciclovia. Definitely recommended!
Megasport shop website – bike rental, cycling tours – Megasport Algarve Blog
Algarve bike holidays – bike rental, self guided holidays for road cyclists, daily MTB and road bike guided tours
Bike shops and mechanics
Here you can find an updated list of bike shops in Portugal: https://pedalportugal.com/directory-links/bike-shops-mechanics/