A stochastic hybrid system can express complex dynamical systems such as biological systems and communication networks, but computation for analysis and control is frequently difficult. In this paper, for a class of stochastic hybrid systems, a discrete abstraction method in which a given system is transformed into a finite-state system is proposed based on the notion of bounded bisimulation. In the existing discrete abstraction method based on bisimulation, a computational procedure is not in general terminated. In the proposed method, only the behavior for the finite time interval is expressed as a finite-state system, and termination is guaranteed. Furthermore, analysis of genetic toggle switches is also discussed as an application.