Electroconvection (EC) phenomena are reported in the uniaxial and biaxial nematic phases of a bent-core liquid crystal. Two EC instabilities are observed. Prewavy_1, which exists only in the uniaxial phase, has stripes parallel to the rubbing direction, a periodicity of order of the device thickness, and an onset voltage that diverges near the uniaxial to biaxial transition. The prewavy_2 instability, characterized by stripes perpendicular to the rubbing direction and a periodicity of twice the device thickness, exists across the entire nematic regime. Our observations are explained through changes in the electrical conductivity anisotropy at the uniaxial to biaxial transition.