That's simple. Instead of writing HTML code straight away in the template, you should put it in some variable in bb_plugins.php. This variable will have an empty value, if the user ID condition is not met; value of HTML code otherwise. Example below.
I think you must tie up this solution also with one you have requested here
. ;-) So certain users not only won't see the button, but also are prohibited use some functional code from bb_codes.php