Partial and total cross sections for electron capture in collisions of B + ions with H atoms from 100 meV/amu to 10 keV/amu have been rigorously determined by using the molecular-orbital expansion method modified by the inclusion of electron translation factors. Quantum-mechanical (3 channels) and semiclassical (12 channels) methods have been employed at collision energies lower than 30 eV/amu and higher than 15 eV/amu, respectively. The agreement of the present results with measurements above 1 keV/amu is reasonable. In our cross sections for the singlet manifold, rather large oscillatory structures are found below 10 eV/amu that are attributable to Stueckelberg-type oscillation. At collision energies below a few eV/amu, the B +(1s3d) and B +(1s3p) states are the dominant states for the triplet and singlet manifolds, respectively. However, the B'+(1s3p) state for the triplet and B +(1s3d) state for the singlet take over' above these energies. At energies above 1 keV/amu, three states, the B +(1s3s), B +(1s3p), and B +(1s3d) states, contribute equally to the electron-capture process. A comparison of the present B + results with previous results for different projectiles with the same charge (i.e., Be +, C +, and N +) reveals that although the cross sections of all these systems lie roughly within a certain range of magnitudes at intermediate collision energies (E =0.5-10 keV/amu), differences begin to emerge in magnitude and energy dependence below this energy. We examined the scalability of the cross section; some remarks on the scaling are given.