This paper concerns the long-time dynamics of a thermoelastic Bresse system with mass diffusion. We prove the existence of a global attractor by showing that the system is gradient and asymptotically smooth. In addition, the attractor is characterized as an unstable manifold of the set of stationary solutions. The quasi-stability of the system and the finite fractal dimension of the global attractor are established by a stabilizability inequality. Finally, we prove the upper semicontinuity of the global attractor regarding the parameter in a dense residual set.