Estimating the abundance of unmarked animal populations from acoustic data is challenging due to the inability to identify individuals and the need to adjust for observation biases including detectability (false negatives), species misclassification (false positives), and sampling exposure. Acoustic surveys conducted along mobile transects were designed to avoid counting individuals more than once, where raw counts are commonly treated as an index of abundance. More recently, false-positive abundance models have been developed to estimate abundance while accounting for imperfect detection and misclassification. We adapted these methods to model summertime abundance and trends of three species of bats at multiple spatial scales using acoustic recordings collected along mobile transects by partners of the North American Bat Monitoring Program (NABat) from 2012 to 2020. This multiscale modeling spanned individual transect routes, larger NABat grid cells (10 km × 10 km), and across the entire extent of modeled species ranges. We estimated relationships between species abundances and a suite of abiotic and biotic predictors (landcover types, climatological variables, physiographic diversity, building density, and the impacts of white-nose syndrome [WNS]) and found varying levels of support between species. We present clear evidence of substantial declines in populations of tricolored bats (Perimyotis subflavus) and little brown bats (Myotis lucifugus), declines that corresponded in space and time with the progression of WNS, a devastating disease of hibernating bats. In contrast, our analysis revealed that similar population-wide declines probably have not occurred in big brown bats (Eptesicus fuscus), a species known to be less affected by WNS. This study provides the first abundance-based species distribution predictions and population trends for bats in their summer ranges in North America. These models will probably be applicable to assessing wildlife populations in other monitoring programs where acoustic data are used or where false-negative and false-positive detections are present. Finally, our abundance framework (as a spatial point pattern process) can serve as a foundation from which more sophisticated integrated species distribution models that incorporate additional streams of monitoring data (e.g., stationary acoustics, captures) can be developed for North American bats.