As far as I know it's not possible to map the F keys on a bluetooth keyboard to an app in iOS. Some keyboards do use the F keys for special functions on the iPad, but these are usually mapped at the OS/hardware level, and not available for use within apps.
For instance, on the Logitech keyboard I bought today the F1 key works as the Home button, and the F12 key switches between keyboards mapping (English and Español with my setup).
How are you accessing the payroll app/program? Through a web browser or using a remote desktop app. There are apps that have virtual keyboards for both categories, and those 'might' support F keys.