Bridge seismic isolation strategy is based on the reduction of shear forces transmitted from the superstructure to the piers by two means: shifting natural period and earthquake input energy reduction by dissipation concentrated in protection devices. In this paper, a stochastic analysis of a simple isolated bridge model for different bridge and device parameters is conducted to assess the efficiency of this seismic protection strategy. To achieve this aim, a simple nonlinear softening constitutive law is adopted to model a wide range of isolation devices, characterized by only three essential mechanical parameters. As a consequence of the random nature of seismic motion, a probabilistic analysis is carried out and the time modulated Kanai-Tajimi stochastic process is adopted to represent the seismic action. The response covariance in the state space is obtained by solving the Lyapunov equation for a stochastic linearized system. After a sensitivity analysis, the failure probability referred to extreme displacement and the mean value of dissipated energy are assessed by using the introduced stochastic indices of seismic bridge protection efficiency. A parametric analysis for protective devices with different mechanical parameters is developed for a proper selection of parameters of isolation devices under different situations.