We report on the experimental observation of stochastic resonance (SR) in a nonGaussian active bath without any periodic modulation. A Brownian particle hopping in a nanoscale double-well potential under the influence of nonGaussian correlated noise, with mean interval tau(P) and correlation time tau(c), shows a series of equally-spaced peaks in the residence time distribution at integral multiples of tau(P). The strength of the first peak is found to be maximum when the mean residence time (tau)(d) matches the double condition, 4 tau(c) asymptotic to tau(P) asymptotic to(tau)(d)/2, demonstrating a new type of bona fide SR. The experimental findings agree with a simple model that explains the emergence of SR without periodic modulation of the double-well potential. Additionally, we show that generic SR under periodic modulation, known to degrade in strongly correlated continuous noise, is recovered by the discrete nonGaussian kicks.