Modulation of donor electron wavefunction via electric fields is vital to quantum computing architectures based on donor spins in silicon. For practical and scalable applications, the donor-based qubits must retain sufficiently long coherence times in any realistic experimental conditions. Here, we present pulsed electron spin resonance studies on the longitudinal (T-1) and transverse (T-2) relaxation times of phosphorus donors in bulk silicon with various electric field strengths up to near avalanche breakdown in high magnetic fields of about 1.2 T and low temperatures of about 8 K. We find that the T-1 relaxation time is significantly reduced under large electric fields due to electric current, and T-2 is affected as the T-1 process can dominate decoherence. Furthermore, we show that the magnetoresistance effect in silicon can be exploited as a means to combat the reduction in the coherence times. While qubit coherence times must be much longer than quantum gate times, electrically accelerated T-1 can be found useful when qubit state initialization relies on thermal equilibration.