The thumb.php timthumb script/file is already whitelisted in the BPS root .htaccess file code, BUT depending on how your theme is calling that thumb.php script/file you may need to add an additional theme skip/bypass rule:
https://forum.ait-pro.com/forums/topic/images-not-displaying-after-bulletproof-security-free-plugin-was-enabled-and-configured/#post-9288
1. Copy this .htaccess code below to this BPS Root Custom Code text box: CUSTOM CODE PLUGIN/THEME SKIP/BYPASS RULES:.
2. Click the Save Root Custom Code button.
3. Go to the Security Modes page, click the Create secure.htaccess File AutoMagic button and Activate Root Folder BulletProof Mode.
Note: Change “Your-Theme-Name” to your actual Theme’s name.
# Theme Thumbnailer script skip/bypass rule
RewriteCond %{REQUEST_URI} ^/wp-content/themes/Your-Theme-Name/thumb\.php [NC]
RewriteRule . - [S=13]