Variable-pole induction machines have high efficiency, high power density, and a wide constant power speed ratio. The pole count must be reconfigured online to maximize these benefits, resulting in a torque disturbance. Existing pole transition approaches trade off transition duration against torque bump. This paper proposes a bumpless, fast pole-changing approach that uses droop control. Constant shaft torque is maintained during the transition by increasing torque in the new configuration at the same rate as the decrease in the previous one. The paper formulates a dynamic model that captures the transition duration and the impact of operating conditions on inverter ratings. Simulations are used to verify the bumpless transition. An experimental 18-leg inverter driving a toroidal machine is used to validate the analysis and test flux transitions as fast as 200 ms. Parameter estimation error and nonlinearities lead to small torque variations within the machine's inherent torque ripple. Tests are performed over several operating conditions to validate the method and analysis and compare it to a conventional ramp approach.