Physical systems with material properties modulated in time provide versatile routes for designing magnetless nonreciprocal devices. Traditionally, nonreciprocity in such systems is achieved exploiting both temporal and spatial modulations, which inevitably requires a series of time-modulated elements distributed in space. In this Letter, we introduce a concept of bianisotropic time-modulated systems capable of nonreciprocal wave propagation at the fundamental frequency and based on uniform, solely temporal material modulations. In the absence of temporal modulations, the considered bianisotropic systems are reciprocal. We theoretically explain the nonreciprocal effect by analyzing wave propagation in an unbounded bianisotropic time-modulated medium. The effect stems from temporal modulation of spatial dispersion effects which to date were not taken into account in previous studies based on the local-permittivity description. We propose a circuit design of a bianisotropic metasurface that can provide phase-insensitive isolation and unidirectional amplification.