Bats host a range of viruses that cause severe disease in humans without displaying clinical symptoms to these infections. The mechanisms of bat adaptation to these viruses are a continuous source of interest but remain largely unknown. To understand the landscape of bat antiviral response in a comprehensive and comparative manner, we studied this response in two bat species - the Egyptian fruit bat and the insectivore Kuhl's pipistrelle, representing the two major bat subordinal clades. We profiled the transcriptional response to dsRNA - that triggers a rapid innate immune response - in skin fibroblasts from a large cohort of replicates from each bat species, using RNAsequencing, and compared bat response with responses in primates and rodents. Both bat species upregulate a similar set of genes, many of which are known to be involved in the antiviral response across mammals. However, a subset of these genes is transcriptionally divergent in response between the two bat species. These transcriptionally divergent genes also evolve rapidly in coding sequence across the bat clade and have particular regulatory and functional characteristics, including specific promoter architectures and association with expression programs thought to underlie tolerance and resistance in response to viral infection. In addition, using single-cell transcriptomics, we show that transcriptionally divergent genes display high expression variability between individual cells. A focused analysis of dsRNA-sensing pathways further points to significant differences between bat and human in basal expression of genes important for triggering antiviral responses. Finally, a survey of genes recently lost or duplicated in bats points to a limited set of antiviral genes that have undergone rapid gene loss or gain in bats, with the latter group resulting in paralogs displaying divergence in both coding sequence and expression in bat tissues. Our study reveals a largely conserved regulatory program of genes upregulated in response to viral infection across bats and other mammals, and points to a set of genes that evolved rapidly in bats through multiple evolutionary mechanisms. This divergence can contribute to bat adaptation to viral infection and provides directions to understanding the mechanisms behind it.