Inside a wordpress plugin which shows a table of posts of the custom type, I added the choice for bulk actions. Aside from the checkboxes I displayed the control for bulk actions, however when I click Apply, nothing happens.

It's said to be an action, I suppose, however i could not find which. I attempted trash_post, however it does not get hit.

How do you execute a bulk remove anyway, since I have no clue if I am even on course.

You'll have to define your bulk actions array inside your class that stretches Wordpress_List_Table then inside your display function you will have to define the person actions.

function get_bulk_actions() {
        $actions = array();

        if ( $this->is_trash )
            $actions['untrash'] = __( 'Restore' );
        else
            $actions['edit'] = __( 'Edit' );

        if ( $this->is_trash || !EMPTY_TRASH_DAYS )
            $actions['delete'] = __( 'Delete Permanently' );
        else
            $actions['trash'] = __( 'Move to Trash' );

        return $actions;
    }

You should use wp_posts_list_table to illustrate what it is done:

$actions = array();
                if ( $can_edit_post && 'trash' != $post->post_status ) {
                    $actions['edit'] = '<a href="' . get_edit_post_link( $post->ID, true ) . '" title="' . esc_attr( __( 'Edit this item' ) ) . '">' . __( 'Edit' ) . '</a>';
                    $actions['inline hide-if-no-js'] = '<a href="#" class="editinline" title="' . esc_attr( __( 'Edit this item inline' ) ) . '">' . __( 'Quick&nbsp;Edit' ) . '</a>';
                }
                if ( current_user_can( $post_type_object->cap->delete_post, $post->ID ) ) {
                    if ( 'trash' == $post->post_status )
                        $actions['untrash'] = "<a title='" . esc_attr( __( 'Restore this item from the Trash' ) ) . "' href='" . wp_nonce_url( admin_url( sprintf( $post_type_object->_edit_link . '&amp;action=untrash', $post->ID ) ), 'untrash-' . $post->post_type . '_' . $post->ID ) . "'>" . __( 'Restore' ) . "</a>";
                    elseif ( EMPTY_TRASH_DAYS )
                        $actions['trash'] = "<a class='submitdelete' title='" . esc_attr( __( 'Move this item to the Trash' ) ) . "' href='" . get_delete_post_link( $post->ID ) . "'>" . __( 'Trash' ) . "</a>";
                    if ( 'trash' == $post->post_status || !EMPTY_TRASH_DAYS )
                        $actions['delete'] = "<a class='submitdelete' title='" . esc_attr( __( 'Delete this item permanently' ) ) . "' href='" . get_delete_post_link( $post->ID, '', true ) . "'>" . __( 'Delete Permanently' ) . "</a>";
                }
                if ( $post_type_object->public ) {
                    if ( in_array( $post->post_status, array( 'pending', 'draft', 'future' ) ) ) {
                        if ( $can_edit_post )
                            $actions['view'] = '<a href="' . esc_url( add_query_arg( 'preview', 'true', get_permalink( $post->ID ) ) ) . '" title="' . esc_attr( sprintf( __( 'Preview &#8220;%s&#8221;' ), $title ) ) . '" rel="permalink">' . __( 'Preview' ) . '</a>';
                    } elseif ( 'trash' != $post->post_status ) {
                        $actions['view'] = '<a href="' . get_permalink( $post->ID ) . '" title="' . esc_attr( sprintf( __( 'View &#8220;%s&#8221;' ), $title ) ) . '" rel="permalink">' . __( 'View' ) . '</a>';
                    }
                }

                $actions = apply_filters( is_post_type_hierarchical( $post->post_type ) ? 'page_row_actions' : 'post_row_actions', $actions, $post );
                echo $this->row_actions( $actions );

                get_inline_data( $post );
                echo '</td>';
            break;

You might also need to include the javascript to create the ajax demands and complete the information in the hidden inline_ div. Have a look or reuse the code from inline-edit-post-dev.js.