A cosmological model with a specific form of the Hubble parameter is constructed in a flat homogeneous, and isotropic background in the framework of $f(R,T)$ gravity, where $R$ is the scalar curvature and $T$ is the trace of the stress-energy-momentum tensor. The proposed functional form of the Hubble parameter is taken in such a way that it fulfills the successful bouncing criteria to find the solution of the gravitational field equations provided the Universe is free from initial singularity. The various constraints on the parameters are involved in the functional form of the Hubble parameter which are analyzed in detail. In addition, we explore physical and geometrical consequences of the model based on the imposed constraints. Furthermore, we demonstrate the bouncing scenario which is realized in our model with some particular values of the model parameters. As a result, we find that all of the necessary conditions are satisfied for a successful bouncing model.