In recent years, the probability density evolution method for structural random dynamic analysis can capture the refined probability density function and its evolution process with regard to both linear and nonlinear, single degree of freedom and multi-degree of freedom structural systems, which provides the satisfactory requirements of accurate structural design and analysis. In this study, firstly, the dimension-reduction simulation method of fully non-stationary mD-nV stochastic vector processes is applied to generate multi-component non-uniform seismic excitation for long-span bridge structures. Secondly, the finite element model of a long-span and high-pier rigid frame bridge with practical engineering background is established. And the representative time-histories of multi-component non-uniform and non-stationary ground motion realized by the dimension-reduction representation are used as random external excitation of the target bridge structure. Then, the probability density evolution method is employed to analyse the refined dynamic response of bridge structure subjected to different seismic excitation conditions. Finally, combined with the equivalent extreme events, the seismic reliability of bridge structure under multi-dimensional non-uniform seismic excitation is investigated. This study verifies the effectiveness of the dimension-reduction representation for simulation realization of multi-support non-uniform ground motion. Meanwhile, the influence of multi-component non-uniform random ground motion on the seismic response and dynamic reliability of long-span and high-pier rigid frame bridge is thoroughly scrutinized, which can provide the basis for the seismic design and analysis of bridge structures.