I notice that BashSupport claims a lot of files that are not really BASH scripts.
Perhaps you could add an option that makes it require a shebang line with some known list of compatible shells (".../sh" or ".../bash", e.g.). I know this is not ideal, since I myself have many non-executable shell scripts used as fragments "source"-ed by other scripts that do not have she-bang lines. Another criterion might be executability (but that, too, excludes my fragment files).
Naturally, I could turn off "Accept files without extensions", but I never give any of my BASH scripts extensions, so that would defeat BashSupport entirely for me.