AppleScript do shell will not work on Application Support directory
If you are hardcoding, without testing if the file exists, then use the following example:

set foo to quoted form of "/Users/vader/someapp.app/Contents/Resources/Scripts/foobar.txt"
set bar to quoted form of "/Library/Application Support/"
try
    do shell script "cp " &amp; foo &amp; space &amp; bar with administrator privileges
end try


If you are calling it from the script within the application bundle,  then use the following example:

on run
    try
        set foo to POSIX path of (path to me as string) &amp; "Contents/Resources/Scripts/foobar.txt"
        set bar to quoted form of "/Library/Application Support/"

        tell application "System Events"
            if exists file foo then
                tell current application
                    do shell script "cp " &amp; quoted form of foo &amp; space &amp; bar with administrator privileges
                end tell
            end if
        end tell
    on error eStr number eNum
        display dialog eStr &amp; " number " &amp; eNum buttons {"OK"} default button 1 with icon caution
        return
    end try
end run




Note: When working with the do shell script command, POSIX pathnames must be used, not aliases. Macintosh HD is not valid in a POSIX path, just in an alias. In a POSIX path of the startup disk, everything starts in the root of the volume: /

Example:

tell application "Finder" to get name of startup disk as alias
tell application "Finder" to get POSIX path of (name of startup disk as alias)


Returns:

Macintosh HD 
/