Living cells are known to generate non-Gaussian active fluctuations that are significantly larger than thermal fluctuations owing to various metabolic activities. Understanding the effect of active fluctuations on various physicochemical processes, such as the transport of molecular motors, is a fundamental problem in nonequilibrium physics. Therefore, we experimentally and numerically study an active Brownian ratchet comprising a colloidal particle in an optically generated asymmetric periodic potential driven by non-Gaussian noise with finite-amplitude active bursts, each arriving at random and decaying exponentially. We determine that the particle velocity is maximum for relatively sparse bursts with finite correlation time and non-Gaussian distribution. These occasional kicks are more efficient for transport and diffusion enhancement of the particle, compared to the incessant kicks of active Ornstein-Uhlenbeck noise. The ratchet reverses its transport direction only when the noise correlation time is shorter than the thermal relaxation time, suggesting possible application in nanoparticle separation.