How to prompt to give specific folder access or full disk access to /bin/bash when run in an app bundle on Catalina?
An way to get around the problem is simply to not invoke /bin/bash, but rather interpret and run the shell script within your own app. For example you could restrict the script language to be a very simple one, so that you do not have to implement full bash scripting functionality (which would be quite an undertaking).
For example if the scripts only consists of simply running literal commands, or perhaps a few conditions - then that could easily be implemented directly in the app, or as a simple language interpreter.
This would then let the user give your app Full Disk Access, and it would work.