Pulsed magnetic resonance allows the quantum state of electronic and nuclear spins to be controlled on the timescale of nanoseconds and microseconds respectively. The time required to flip dilute spins is orders of magnitude shorter than their coherence times, leading to several schemes for quantum information processing with spin qubits. Instead, we investigate 'hybrid nuclear-electronic' qubits consisting of near 50:50 superpositions of the electronic and nuclear spin states. Using bismuth-doped silicon, we demonstrate quantum control over these states in 32 ns, which is orders of magnitude faster than previous experiments using pure nuclear states. The coherence times of up to 4 ms are five orders of magnitude longer than the manipulation times, and are limited only by naturally occurring (29)Si nuclear spin impurities. We find a quantitative agreement between our experiments and an analytical theory for the resonance positions, as well as their relative intensities and Rabi oscillation frequencies. These results bring spins in a solid material a step closer to research on ion-trap qubits.