A couple is taking a break from bicycling.
two people park their bikes.
Two people can have a relationship other than a couple. Taking a break from bicycling does not imply they are parking their bikes.
People can take a break from bicycling without park their bikes.
People may take a break from bicycling and stop moving completely or they may walk their bikes which means they will not park their bikes and the bikes may be their bikes or the bikes may be someone else's.