A completed application can often be modified to fit a second submission, much as a manuscript can be sent to a second publisher if it is rejected by the first. Word processing equipment and spreadsheets may make reworking for later submissions rather quick and easy. University faculty are experienced at grant applications. To make them is part of the job. But even professors get discouraged and fail to make good second and subsequent applications.
Many school districts have an administrator who is charged with being alert to grant opportuniites.
All administrators are aware of the potential of grants to help their schools. It is true that getting a grant can be a pain in the neck. You often have several reports to fill about about the progress of the project. Sometimes going after your idea without money convinces people after a while to put money into it.