We deal with a model that is called Bin Covering with Delivery. Here we search for a “good and fast” covering. This problem has been defined and investigated recently. Here we continue and significantly augment the preliminary investigations of the problem. After studying the goodness of adapted versions of some classical algorithms, we propose a parametrized algorithm and use a heuristic parameter optimization method to solve this (algorithmically very challenging) problem. Namely, we apply local search to determine a good choice of the parameters. The efficiency of the proposed method is demonstrated by intensive computer experiments on appropriate modifications of benchmark instances.