Walker for integration of WordPress custom menu with Bootstrap navbar.

gistfile1.php

<?php

/**
 * Walker for integration of WordPress custom menu with Bootstrap navbar.
 */
class Walker_Navbar_Menu extends Walker_Nav_Menu {

        public $dropdown_enqueued;

        /**
         * Check if required script queued.
         */
        function __construct() {

                $this->dropdown_enqueued = wp_script_is( 'bootstrap-dropdown', 'queue' );
        }

        /**
         * Adjust classes for individual menu items.
         */
        function display_element( $element, &$children_elements, $max_depth, $depth = 0, $args, &$output ) {

                if ( $element->current )
                        $element->classes[] = 'active';

                $element->is_dropdown = ! empty( $children_elements[$element->ID] );

                if ( $element->is_dropdown ) {

                        if( 0 == $depth  )
                                $element->classes[] = 'dropdown';
                        elseif( 1 == $depth )
                                $element->classes[] = 'dropdown-submenu';
                }

                parent::display_element( $element, $children_elements, $max_depth, $depth, $args, $output );
        }

        /**
         * Enqueue script and set class for list.
         */
        function start_lvl( &$output, $depth ) {

                if ( ! $this->dropdown_enqueued ) {
                        wp_enqueue_script( 'bootstrap-dropdown' );
                        $this->dropdown_enqueued = true;
                }

                $indent  = str_repeat( "\t", $depth );
                $class   = ( $depth < 2 ) ? 'dropdown-menu' : 'unstyled';
                $output .= "\n{$indent}<ul class='{$class}'>\n";
        }

        /**
         * Adjust markup for top level dropdown menu item.
         */
        function start_el( &$output, $item, $depth, $args ) {

                $item_html = '';
                parent::start_el( $item_html, $item, $depth, $args );

                if ( $item->is_dropdown && ( 0 == $depth ) ) {
                        $item_html = str_replace( '<a', '<a class="dropdown-toggle" data-toggle="dropdown"', $item_html );
                        $item_html = str_replace( '</a>', '<b class="caret"></b></a>', $item_html );
                        $item_html = str_replace( esc_attr( $item->url ), '#', $item_html );
                }

                $output .= $item_html;
        }
}