We have observed anomalous transport properties for a 50 nm Bi dot in the Coulomb-blockade regime. Over a range of gate voltages, Coulomb blockade peaks are suppressed at low bias, and dramatic structure appears in the current at higher bias. We propose that the state of the dot is determined self-consistently with the state of a nearby two-level system (TLS) to which it is electrostatically coupled. As a gate voltage is swept, the ground state alternates between states of the TLS, leading to skipped Coulomb-blockade peaks at low bias. At a fixed gate voltage and high bias, transport may occur through a cascade of excited states connected by the dynamic switching of the TLS.