wp_enqueue_scripts hook is not being called

Your code is correct, though I would not add the callback if the function name has already been used. If someone else has used the name you don’t know what you might be adding.

if(!function_exists('bi_frontend_scripts')) {
    function bi_frontend_scripts() {
        wp_enqueue_script('jquery');
        // I originally wanted to do:
        wp_enqueue_script('jQuery.bxSlider', get_bloginfo('template_url').'/scripts/jquery.bxslider/jquery.bxslider.min.js', array('jquery'));
    }
    add_action('wp_enqueue_scripts', 'bi_frontend_scripts');
}

I also tested your “hook dump” function– aal_handler()— and that works. wp_enqueue_scripts is part of the output.

I have to conclude that there is something wrong with the theme. wp_enqueue_scripts is hooked to wp_head, which fires in the wp_head() function. The most obvious possibility is that your theme is not using wp_head() correctly, or at all. Another distant possibility is that something has removed your callback– for example, with:

remove_all_filters('wp_enqueue_scripts');