Road cycling is very popular in Spain.
In Nerja with sorroundings are many fine trips to bicycle. In the surrounding mountains are stunning roads that winds through a spectacular natural setting with wonderful views from the road. There are also many fine small mountain villages to stop and explore.
It is fine to take your bike on the flight, check with your airline for regulations concerning packaging and prices.
If you wish to rent a bike instead there is the opportunity for this in Nerja. See below links to bike rentals.
Links Bicycle rental:
(very good shop to rent a bike in with very knowledgeable staff)
Links to various bike routes: