Dynamic bandwidth reservation refers to the process of dynamically updating the bandwidth allocation to a connection between two network end points on the basis of actual aggregate traffic demand of the connection. We assume a scenario in which bandwidth updates for the connection should not be performed too frequently and the frequency of updates are thus limited to a so-called desired update rate. We propose an asynchronous model-free adaptive hysteresis algorithm for dynamic bandwidth reservations with such update frequency constraints. We validate the effectiveness of the proposed approach by comparing its bandwidth efficiency with that of a synchronous model-based dynamic bandwidth reservation mechanism from the existing literature.