Bismuth ferrite, BiFeO3, is the only known room-temperature magnetic ferroelectric material. We demonstrate here, using neutron scattering measurements in high quality single crystals, that the antiferromagnetic and ferroelectric order parameters are intimately coupled. Initially in a single ferroelectric state, our crystals have a canted antiferromagnetic structure describing a unique cycloid. Under electrical poling, polarization reorientation induces a spin flop. We argue here that the coupling between the two orders may be stronger in the bulk than in thin films where the cycloid is absent.