We present a stochastic search algorithm called Wasp beHavior Inspired STochastic SampLING (WHISTLING). Dispatch scheduling policies often provide good decision-making baselines for scheduling problems, but are not infallible and can make suboptimal decisions. Hence, instead of unconditionally following its decisions, we use the dispatch policy to bias a stochastic selection process. WHISTLING provides a fast and effective method for sampling from a stochastic neighborhood of a heuristic solution given a dispatch policy. We have specifically focused our experimentation on a weighted tardiness scheduling problem with sequence-dependent setups.