The dielectric properties of elastomer composites formed by dispersions of bismuth ferrite (BiFeO₃) multiferroic filler particles in styrene-butadiene rubber (SBR) were studied. The SBR/BiFeO₃ films (10-100 µm) were prepared in the presence of electric (E) or magnetic fields (H), showing remarkable characteristics in comparison with systems obtained in its absence. The dispersed multiferroic fillers form clusters of much smaller size when prepared under E or H. The dielectric constant, ε (measured up to 1 MHz), increases with BiFeO₃ concentration until reaching saturation. The rise of ε was obtained at concentrations much lower for samples prepared in the presence of E or H than in its absence. Saturation is assigned to connectivity between filler clusters at the largest concentrations, increasing leakage currents and limiting the dielectric behavior. The whole dependence of ε with BiFeO₃ concentration was described using a proposed model. The dc resistivities, ρ, increase with BiFeO₃ concentration but remain high (ρ ≃ 10 GΩ·cm), allowing using the films as capacitors with filter action between 100 kHz and 7 MHz. The films prepared in the presence of H present strong dependence of the ferroelectric response with magnetic fields applied after preparation; that is, electromagnetic coupling was observed in those samples.