Let f_m,n,h be the number of spanning forests with h edges in the complete bipartite graph K_m,n. Kirchhoff's Matrix Tree Theorem implies f_m,n,m+n-1=m^n-1 n^m-1 when m ≥1 and n ≥1, since f_m,n,m+n-1 is the number of spanning trees in K_m,n. In this paper, we give an algorithm for computing f_m,n,h for general m,n,h. We implement this algorithm and use it to compute all non-zero f_m,n,h when m ≤50 and n ≤50 in under 2 days.