The electric dipole moments (mu) of BH and HF are computed in conventional calculations employing different correlation-consistent basis sets at the levels of Hartree-Fock theory, second-order perturbation theory, and coupled cluster theory with single and double excitations, and single and double excitations with a perturbative triples correction. The basis-set convergence of mu is examined by comparison with results obtained with explicitly correlated wave function models. Inclusion of diffuse functions in the basis set is essential for accurate calculations of mu. They speed up the convergence at the Hartree-Fock level significantly and make the convergence at the correlated levels systematic. Once the outer valence regions important for mu are described accurately via the diffuse functions, the convergence at the correlated levels is governed by the interelectronic Coulomb singularity. For the aug-cc-pVXZ basis sets, the correlation contribution to mu follows mu(X)(corr)=mu(lim)(corr)+aX(-3), which is similar to the form for the correlation energy, and extrapolated values based on this form represent a significant improvement on the ordinary basis-set results. Our estimates of the exact dipole moments mu(e(HF))=1.8037 +/- 0.0007 D and mu(0(BH))=1.3586 +/-0.0007 D are in excellent agreement with the experimental values mu(e(HF))=1.803 +/- 0.002 D and mu(0(BH))=1.27 +/- 0.21 D.