The antiferromagnetic Ising model samples subsets of vertices of a graph with weight decaying exponentially in the number of edges induced. We study the problem of sampling from this model on the class of bipartite, regular graphs with good vertex expansion. We show that a natural sampler, namely the Glauber dynamics, mixes exponentially slowly in a wide range of parameters. On the other hand, we give an efficient alternative algorithm for sampling from the Ising model and an FPTAS for its partition function, using polymer models and the cluster expansion method.