The effects of two kinds of time-delayed feedbacks and non-Gaussian coloured noise on modulating bifurcations in a birhythmic model have been investigated. The non-Gaussian coloured noise is approximated asan Ornstein–Uhlenbeck process using the path integral approach. Subsequently, by the conjoint of the multiscale method and random average technique, the stationary probability density function (SPDF) of the amplitude is obtained. It is concluded that either in the condition of determinacy or randomness, time delays can effectively control birhythmicity. Especially considered the presence of noise, the varying displacement delay results in multiple bifurcation in the case of single delay, while the velocity delay triggers more complex bifurcation behaviour in the case of double delays. The strength and correlation time of noise present the opposite impacts on bifurcation, so do the two delayed coefficients. Bifurcation under different excitations is analysed theoretically, and the correctness is verified by numerical simulation. Many abundant bifurcations are available by adjusting the time-delayed feedbacks and noise intensity, which may be conductive to achieve the expected phenomenon in the enzymatic–substrate reactions.