Federated athletes are allowed to leave their municipality to travel anywhere in the country to train or compete for their sport, as long as it is not in the curfew hours (top level basketball and football which can disobey the curfew)
Basically the same rule that let's professional athlete's go about their business is defined in the BOJA and BOE as being a federated athletes. In terms of cycling the cycling federation has defined that as anybody who has a race licence (or judge or trainer with a licence). You can buy the licence and many amateurs (myself included) have one as it is an easy way of getting insurance. So that little bit of plastic let's me cycle anywhere I want in the country...it also let's me put my bike in the back of the car and go wherever I want 'to train. Other sports are available...my wife is thinking about joining the tiddlywinks federation if she can find it!