We report the occurrence of bursting oscillations in a gyroscope oscillator driven by low-frequency external period forcing. The bursting patterns arise when either the frequency or amplitude of the excitation force is varied. They take the form of pulse-shaped explosions (PSEs) wherein periodic attractors of lower periodicity disappear due to the loss of asymptotic stability of the equilibrium point between resting and active states. The process involves the appearance of zero eigenvalues and the creation of new attractors of higher periodicity. Both point-cycle and cycle-cycle bursting is seen. It is accompanied by the birth of periodic attractors, ranging from period one to period four, depending on an integer n in the frequency of the parametric driving force. The dynamics of the oscillator is shown to exhibit a fold bifurcation related to critical escape transitions.