How to add “Stick this post to the front page” to front end?

I think this small source code is your solution. It currently doesn’t have frontend feedback for the Sticky Post change, but you can enhance this string, class or whatever you want in the function fb_stick_post.

The first function adds the item in the Admin Bar and creates a new Url with a param value. Also, on click calls a function to read the Url param and, if it’s true, then do the change to the sticky status of this post id.

add_action( 'admin_bar_menu', 'fb_add_admin_bar_sticky', 35 );
function fb_add_admin_bar_sticky() {
    global $wp_admin_bar;

    if ( ! is_super_admin() || ! is_admin_bar_showing() )
        return;

    $current_object = get_queried_object();
    if ( empty($current_object) )
        return;

    if ( ! empty( $current_object->post_type ) && 
        ( $post_type_object = get_post_type_object( $current_object->post_type ) ) && 
        current_user_can( $post_type_object->cap->edit_post, $current_object->ID ) 
    ) {
        $wp_admin_bar->add_menu( 
            array(
                'id' => 'sticky_post', 
                'title' => __('Sticky'), 
                'href' => get_permalink() . '?stick_post=true', 
                'meta' => array(
                    'title' => __( 'Click me' ),
                    'onclick' => fb_stick_post( get_the_ID() )
                )
            )
        );
    }
}

function fb_stick_post( $post_id ) {

    if ( isset($_GET['stick_post']) && 'true' == htmlspecialchars( $_GET['stick_post'] ) )
        stick_post( $post_id );
}

Update 07/30/2012

Now an small plugin with easy solution. The plugin adds an item inside the Admin Bar. The string of the button check for is sticky and give the possibility to stick or unstick the current post.

I change the hook for add the admin bar item to ´template_redirect` for use an redirect after update the stick flag on post.

<?php
/**
 * Plugin Name: Stick/Unstick post via Admin bar
 * 
 */

if ( ! function_exists( 'fb_add_admin_bar_sticky' ) ) {

    add_action( 'template_redirect', 'fb_add_admin_bar_sticky' );
    function fb_add_admin_bar_sticky() {
        global $wp_admin_bar;

        if ( ! is_super_admin() || ! is_admin_bar_showing() )
            return;

        $current_object = get_queried_object();
        if ( empty($current_object) )
            return;

        if ( ! empty( $current_object->post_type ) && 
            ( $post_type_object = get_post_type_object( $current_object->post_type ) ) && 
            current_user_can( $post_type_object->cap->edit_post, $current_object->ID ) 
        ) {

            // check, if an sticky post
            if ( is_sticky( get_the_ID() ) ) {
                $title = __('Unsticky');
                $link = '?unstick_post=true';
                $attr_title = __( 'Make this post unsticky' );
            } else {
                $title = __('Sticky');
                $link = '?stick_post=true';
                $attr_title = __( 'Make this post sticky' );
            }

            $wp_admin_bar->add_menu(
                array(
                    'id' => 'sticky_post', 
                    'title' => $title, 
                    'href' => get_permalink() . $link, 
                    'meta' => array(
                        'title' => $attr_title,
                        'onclick' => fb_stick_post( get_the_ID() )
                    )
                )
            );
        }
    }

    function fb_stick_post( $post_id ) {

        if ( isset($_GET['stick_post']) && 'true' == htmlspecialchars( $_GET['stick_post'] ) ) {
            stick_post( $post_id );
            wp_redirect( get_permalink( $post_id ) );
            exit();
        }

        if ( isset($_GET['unstick_post']) && 'true' == htmlspecialchars( $_GET['unstick_post'] ) ) {
            unstick_post( $post_id );
            wp_redirect( get_permalink( $post_id ) );
            exit();
        }
    }

}

or download this plugin Gist 3214922