Is there a shortcut to change bulk BMP images to JPG images in a site?

Assuming you add the files with the matching filenames in the appropriate wp-content/uploads/ folders you could run a few SQL queries to update the WordPress database to use the .jpg files.

Assuming your wpdb prefix is wp these queries would be:

UPDATE wp_posts SET post_mime_type = replace(post_mime_type, 'image/bmp','image/jpeg');

UPDATE wp_posts SET guid = replace(guid, '.bmp','.jpg');

UPDATE wp_postmeta SET meta_value = replace(meta_value, '.bmp','.jpg');