Let G = (V,E) be a graph in which every vertex v ∈ V has a weight w(v) ≥ 0 and a cost c(v) ≥ 0. Let SG be the family of all maximum-weight stable sets in G. For any integer d ≥ 0, a minimum d-transversal in the graph G with respect to SG is a subset of vertices T ⊆ V of minimum total cost such that |T ∩S| ≥ d for every S ∈ SG. In this paper, we present a polynomial-time algorithm to determine minimum d-transversals in bipartite graphs. Our algorithm is based on a characterization of maximum-weight stable sets in bipartite graphs. We also derive results on minimum d-transversals of minimum-weight vertex covers in weighted bipartite graphs.