We present detailed neutron-scattering studies of the magnon dispersion curve in Bi2CuO4. We show the existence of a single doubly degenerate dispersion branch. In this antiferromagnetic S = 1/2 system, we found that our experimental results are totally accounted for by a model of four superexchange interactions: J1 = 2.2 +/- 0.15; J2 = 0.7 +/- 0.05; J3 = 0.2 +/- 0.05; J4 = 0.8 +/- 0.05; and anisotropy constant D = 0.3 +/- 0.05 in meV. These Cu-Cu interactions are similar to those between the two CuO2 planes of the so-called bilayer of YBa2Cu3O6+x, and this work is a direct determination of such couplings in copper oxides.