#fixme {position: fixed;left: 0;right: 0; top:0;}
/* prevent overlap */
body{padding-top:70px;}

<div id="fixme">
    <div class="container">
         <!-- your navbar here -->
    </div>
</div>

.navbar-default {
    background-color:transparent;
    border: none;
}

.navbar > .container > div
{
  background-color: pink;

}

<div class="navbar navbar-default navbar-fixed-top">
      <div class="container">
          <div>
        <div class="navbar-header">
          <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">
            <span class="icon-bar"></span>
            <span class="icon-bar"></span>
            <span class="icon-bar"></span>
          </button>
          <a class="navbar-brand" href="#">Project name</a>
        </div>
        <div class="navbar-collapse collapse">
          <ul class="nav navbar-nav">
            <li class="active"><a href="#">Home</a></li>
            <li><a href="#about">About</a></li>
            <li><a href="#contact">Contact</a></li>
            <li class="dropdown">
              <a href="#" class="dropdown-toggle" data-toggle="dropdown">Dropdown <b class="caret"></b></a>
              <ul class="dropdown-menu">
                <li><a href="#">Action</a></li>
                <li><a href="#">Another action</a></li>
                <li><a href="#">Something else here</a></li>
                <li class="divider"></li>
                <li class="dropdown-header">Nav header</li>
                <li><a href="#">Separated link</a></li>
                <li><a href="#">One more separated link</a></li>
              </ul>
            </li>
          </ul>
          <ul class="nav navbar-nav navbar-right">
            <li><a href="../navbar/">Default</a></li>
            <li><a href="../navbar-static-top/">Static top</a></li>
            <li class="active"><a href="./">Fixed top</a></li>
          </ul>
        </div><!--/.nav-collapse -->
        </div>
        </div>
    </div>

.navbar-default{
    background-image: none;
    -webkit-box-shadow: none;
    border-style : none;
    background-color: white; // the color i chose
 }

$(document).ready(function () {
    var siteWidth = $('.container').width();
    $('.navbar').width(siteWidth);
});