We consider a natural, yet seemingly not much studied, extremal problem in bipartite graphs. A bi-hole of size t in a bipartite graph G is a copy of K t,t in the bipartite complement of G. Let f (n, ∆) be the largest k for which every n×n bipartite graph with maximum degree ∆ in one of the parts has a bi-hole of size k. Determining f (n, ∆) is thus the bipartite analogue of finding the largest independent set in graphs with a given number of vertices and bounded maximum degree. Our main result determines the asymptotic behavior of f (n, ∆). More precisely, we show that for large but fixed ∆ and n sufficiently large, f (n, ∆) = Θ( log ∆ ∆ n). We further address more specific regimes of ∆, especially when ∆ is a small fixed constant. In particular, we determine f (n, 2) exactly and obtain bounds for f (n, 3), though determining the precise value of f (n, 3) is still open.