Meaning of Error: Cannot redeclare bootstrap_preprocess_region()
This was happening because I'd copied .func.php files from the templates folder of the Bootstrap parent theme into my base theme alongside .tpl.php files. Bootstrap is relatively unusual in that it has files in the templates folder alongside tpl files that will break the site if they're treated like standard theme tpl files.

While the .tpl.php files are to be copied as normal, to override the contents of the other files, you are expected to copy their appropriate contents into your subtheme's template.php file or into a new .func.php file, and substitute your subtheme name for the bootstrap part of the function name.

There's some more information on the theme registry docs page.