In performance-based seismic assessment, structural response is characterised with increasing seismic intensity via some form of intensity measure (IM). IMs are typically related to the characteristics of ground shaking and dynamic properties of the structure, with spectral acceleration at the first and dominant mode of vibration being a popular choice in the case of buildings. In bridge structures, where no single dominant mode typically exists for bridges with any degree of irregularity, the use of spectral acceleration at one single mode of vibration may be somewhat inefficient due to a more multi-modal transverse structural response. To counter this and also to appease the needs of bridge portfolio assessment, where a group of structures is assessed collectively to evaluate entire bridge networks, peak ground acceleration has become a popular IM, albeit its drawbacks in terms of meaning with respect to structural dynamics. To address these limitations, this paper explores the use of different IMs for a more efficient assessment of bridges. Among these, there is average spectral acceleration, whereby a pertinent period range is used to define the IM that could suit the needs of a bridge structure with multi-modal response as well as when more than one bridge structure is considered. To do this, a number of bridges are considered and evaluated via incremental dynamic analysis for different IMs. The results show that average spectral acceleration is indeed a quite efficient IM that can lead to a more refined quantification of bridge performance, both individually and also as part of a larger bridge network when conducting portfolio risk assessment.