We propose new designs of plasmonic modulators, which can be used for dynamic signal switching in photonic integrated circuits. We study performance of a plasmonic waveguide modulator with bismuth ferrite as a tunable material. The bismuth ferrite core is sandwiched between metal plates (metal-insulator-metal configuration), which also serve as electrodes. The core changes its refractive index by means of partial in-plane to out-of-plane reorientation of ferroelectric domains in bismuth ferrite under applied voltage. As a result, guided modes change their propagation constant and absorption coefficient, allowing light modulation in both phase and amplitude control schemes. Due to high field confinement between the metal layers, existence of mode cut-offs for certain values of the core thickness, and near-zero material losses in bismuth ferrite, efficient modulation performance is achieved. For the phase control scheme, the π phase shift is provided by a 0.8-μm long device with propagation losses 0.29 dB/μm. For the amplitude control scheme, up to 38 dB/μm extinction ratio with 1.2 dB/μm propagation loss is predicted.