Bats do not eat mosquitoes, not on purpose. That is a myth that has since been found to be false. Biologists have been analyzing bat guano for years, in order to determine diet, and no species of bat has been found with much, if any, mosquito parts in their feces.
When a bat feeds, it does so in order to store up fat for the upcoming winter hibernation. A mosquito is tiny and has no sustenance to it at all- why would a bat waste energy for such an insignificant meal? It would have to consume thousands, or more, of mosquitoes per night to even make the effort worth it. When bats hunt they are going after moths and beetles, and any mosquitoes they consume are eaten accidentally.