The cross-section ratio \(R_{\mathrm{b}} = \sigma( \rm e^+ e^- \to{\rm b\overline{\rm b}} )/\sigma(\rm e^+ e^-\to{\mathrm q\bar{\mathrm q}} )\) and the bottom and charm forward-backward asymmetries \(A_{\mathrm{FB}}^{\mathrm{b}}\) and \(A_{\mathrm{FB}}^{\mathrm c}\) are measured using event samples collected by the OPAL detector at centre-of-mass energies between 130 and 189 GeV. Events with bottom quark production are selected with a secondary vertex tag, and a hemisphere charge algorithm is used to extract \(A_{\mathrm{FB}}^{\mathrm{b}}\). In addition, the bottom and charm asymmetries are measured using leptons from semileptonic decays of heavy hadrons and pions from \(\mathrm{D}^{*+}\to\rm D^0{\pi^+}\) decays. The results are in agreement with the Standard Model predictions.