A bicycle component control apparatus is basically provided with a power supply sensor and a controller. The power supply sensor detects a power level of a power supply being supplied from the power supply to two electrical bicycle components. The controller operates the two electrical bicycle components in response to receiving at least one signal from at least one input member. The controller operates the two electrical bicycle components at different starting times while the power level is below a prescribed power level. The controller is configured to simultaneously operate the two electrical bicycle components while the power level is above the prescribed power level.