The density field of optically selected galaxies within 8000 km s-1 is used to predict the peculiar velocities of Dn-σ and IRTF galaxies employing linear gravitational instability theory. To obtain acceptable fits to the observed peculiar velocities in the CMB frame, it is necessary to fit two parameters: B0 = Ω0.6b0-1(where b0 is a biasing parameter for optical galaxies), which scales the predictions of the optical density field within 8000 km s-1; and a residual bulk motion due to sources outside the volume. The fits yield β0 = 0.50+/-0.06(1σ random errors) for both the IRTF and the Dn-σ samples, and a residual bulk motion of 405+/-45 km s-1 towards l = 292deg, b= 7deg for the IRTF field galaxies. There is no evidence for a mass concentration in the zone of avoidance within 8000 km s-1 whose effect on the Local Group is more than 100 km s-1, so the residual bulk motion must be due primarily to sources beyond 8000 km s-1. The result for β0 corresponds to Ω = 0.32 +/- 0.06 if mass traces light(b0 = 1), or to b0 = 2.0+/-0.24 if Ω = 1. If biasing is independent of scale, then taken together these results are inconsistent with the predictions of the standard cold dark matter cosmology for any choice of the biasing parameter, but are compatible with cosmological models that fit the galaxy number counts on large scales.