Using the combined CLEO II and CLEO II.V data sets of 9.1 fb(-1) at the Upsilon(4S), we measure properties of psi mesons produced directly from decays of the B meson, where "B" denotes an admixture of B+, B-, B0, and B;(0), and "psi" denotes either J/psi(1S) or psi(2S). We report first measurements of psi polarization in B-->psi(direct)X: alpha(psi(1S))=-0.30(+0.07)(-0.06)+/-0.04 and alpha(psi(2S))=-0.45(+0.22)(-0.19)+/-0.04. We also report improved measurements of the momentum distributions of psi produced directly from B decays, correcting for measurement smearing. Finally, we report measurements of the inclusive branching fraction for B-->psiX and B-->chi(c1)X.