The structure and stability of clusters of a boron atom with one to eight H-2 molecules is investigated. For the simplest BH2 clusters, the lowest ab initio adiabatic potentials for o-H-2 and p-H-2 interacting with a boron atom are used. For the larger clusters (n=2-8), the p-Hz is treated as a sphere, and the total potential is taken to be the sum of pairwise additive B-H-2 and H-2-H-2 interactions which include, in the former case, an anisotropy due to the orientation of the unpaired B 2p electron. This electronic interaction is considerably more attractive when H-2 approaches the B atom in a plane perpendicular to the orientation of the 2p orbital. The local and global minima on these potential surfaces were located and diffusion quantum Monte Carlo simulations were used to determine the energies and properties of the ground state wave functions for these B-(H-2)(n) clusters. For the B(H-2) cluster, a comparison is made with the results of variational calculations.