Prevent replacing  with
If I'm reading the question directly, you've copied button.func.php into your sub-theme, modified the code inside it, and then tried to see if your changes work?

If that's what you did, the problem is that Drupal never sees the code. Fortunately (if that is the problem) the solution is simple: copy the code from that file into your sub-theme's template.php file and make whatever changes are required. Be sure the function is correctly named (i.e. to override theme_button, you'd need themename + button = themename_button()). In your example above, your sub-theme would have to be named 'bootstrap_subtheme_adl_admin' in order for your function to be called even if the code is in the correct file.



Incidentally, the reason the button.func.php file works in the base Bootstrap theme appears to be the theme's registry.inc file.



Basic sub-theme how-to with Bootstrap


Download Bootstrap sub theme into /sites/all/themes; don't bother to enable the theme
Copy bootstrap_subtheme from the /sites/all/themes/bootstrap/bootstrap_subtheme to /sites/all/themes/bootstrap_subtheme
Move /sites/all/themes/bootstrap_subtheme/bootstrap_subtheme.info.starterkit to /sites/all/themes/bootstrap_subtheme/bootstrap_subtheme.info
Enable bootstrap_subtheme


Overriding a theme function implemented by a parent theme


Set up parent and subtheme as described above
Never edit the parent theme in any way
Copy the theme function you want to modify from e.g. /sites/all/themes/bootstrap/theme/system/button.func.php into the file at /sites/all/themes/bootstrap_subtheme/template.php
Change the name of the function in /sites/all/themes/bootstrap_subtheme/template.php from bootstrap_button to bootstrap_subtheme_button