In this paper we consider the Bounded Length Median Path Problem which can be defined as the problem of locating a path-shaped facility that departures from a given origin and arrives at a given destination in a network. The length of the path is assumed to be bounded by a given maximum length. At each vertex of the network (customer-point) the demand for the service is given and the cost to reach the closest service-point is computed. The objective is to minimize the sum of these costs over all the customer-points in the network. We consider two local search metaheuristics, the well known Tabu search and the Old bachelor acceptance and we propose a comparative analysis of the performances of the two procedures. We implement streamlined versions of Tabu search and Old bachelor acceptance. Our main concern is to provide knowledge about the intrinsic strategy adopted by each metaheuristic and to know whether one is more appropriate than the other for our problem.