Potential energy curves for the interaction of B+ (S-1) with RG (S-1), RG = He-Rn, have been calculated at the CCSD(T) level of theory employing quadruple-zeta and quintuple-zeta quality basis sets. The interaction energies from these curves were subsequently point-by-point extrapolated to the basis set limit. Rovibrational energy levels have been calculated for each extrapolated curve, from which spectroscopic parameters are determined. These are compared to previously determined experimental and theoretical values. The potentials have also been employed to calculate the transport coefficients for B+ traveling through a bath of RG atoms. We also investigate the interactions between B+ and the rare gases via contour plots, natural population analysis (NPA), and molecular orbital diagrams. In addition, we consider the atoms-in-molecules (AIM) parameters. The interactions here are compared and contrasted with those for Li+-He and B+-RG; it is concluded that there is significant and increasing dative covalent bonding for the Be+-RG and B+-RG complexes for RG = Ar-Rn, while the other species are predominantly physically bound.