functions.php

<?php

/**
 * Register AMP Menu
 *
 */
function ea_register_amp_menu() {
  register_nav_menu( 'amp-header', 'AMP Header' );
}
add_action( 'after_setup_theme', 'ea_register_amp_menu' );

/**
 * Load header file from our theme
 *
 */
function ea_amp_header( $file, $type, $post ) {
  if( 'header-bar' == $type ) {
    $file = get_stylesheet_directory() . '/amp-templates/header-bar.php';
  }
  return $file;
}
add_filter( 'amp_post_template_file', 'ea_amp_header', 10, 3 );

/**
 * Header CSS 
 *
 */
function ea_amp_header_css() {
  // only CSS here please...
  ?>
  .amp-wp-title-bar {
    background: #3daad4;
    height: 68px;
  }

  .amp-wp-title-bar a {
    color: #fff;
    text-decoration: none;
  }

  .amp-wp-title-bar a.logo {
    height: 68px;
    line-height: 68px;
  }

  .amp-wp-title-bar .nav-header {
    float: right;
    width: auto;
  }

  .amp-wp-title-bar .nav-header .mobile-open,
  .amp-wp-title-bar .nav-header .mobile-close {
    display: none;
  }

  .amp-wp-title-bar .nav-header ul {
    margin: 0;
    padding: 0;
  }

  .amp-wp-title-bar .nav-header li {
    display: block;
    list-style-type: none;
    float: left;
  }

  .amp-wp-title-bar .nav-header a {
    display: block;
    padding: 20px;
    font-family: sans-serif;
  }

  @media only screen and (max-width: 767px) {

    .amp-wp-title-bar {
      height: auto;
    }

    .amp-wp-title-bar .nav-header {
      float: none;
      overflow: hidden;
      width: 100%;
    }

    .amp-wp-title-bar .nav-header ul {
      height: 0;
    }

    .amp-wp-title-bar .nav-header:hover ul {
      height: auto;
    }

    .amp-wp-title-bar .nav-header .mobile-open {
      position: absolute;
      top: 0;
      right: 0;
      display: block;
      color: #fff;
      font-size: 18px;
      padding: 20px;
      cursor: pointer;
    }

    .amp-wp-title-bar .nav-header li {
      float: none;
    }

    .amp-wp-title-bar .nav-header a {
      padding: 10px 16px;
      text-align: center;
    }

  }


  <?php
}
add_action( 'amp_post_template_css', 'ea_amp_header_css' );

header-bar.php

<div class="amp-wp-title-bar">
	<div class="wrap">
		<a class="logo" href="<?php echo esc_url( $this->get( 'home_url' ) ); ?>">
			<?php echo esc_html( $this->get( 'blog_name' ) ); ?>
		</a>
		<?php
		if( has_nav_menu( 'header' ) ) {
			echo '<nav class="nav-header"><div class="mobile-open">&#9776;</div>';
			wp_nav_menu( array( 'theme_location' => 'header', 'container' => 'false', 'depth' => 1 ) );
			echo '</nav>';
		}
		?>
	</div>
</div>