bootstrap - how to put your navbar on top of your background image?

You need to remove the background from your nav-bar:

.navbar-default {
    background: none;
}

<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" rel="stylesheet"/>

<style>
html,
body {
  height: 100%;
	background: red;
}

.navbar-default {
    background: none;
  	border: none;
}
</style>

<!-- Wrap all page content here -->
<div id="wrap">
  
  <!-- Fixed navbar -->
  <div class="navbar navbar-default navbar-fixed-top">
    <div class="container">
      <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="collapse navbar-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>
      </div><!--/.nav-collapse -->
    </div>
  </div>
  
</div>

Bootstrap 4

The Navbar has no background color, so it's transparent by default. Just remember to use navbar-light or navbar-dark so the link colors work with the contrast of the background image. Display of the toggler is also based on navbar-(dark or light).

https://www.codeply.com/go/FTDyj4KZlQ

<nav class="navbar navbar-expand-sm fixed-top navbar-light">
    <div class="container">
        <button class="navbar-toggler navbar-toggler-right" type="button" data-toggle="collapse" data-target="#navbar1">
            <span class="navbar-toggler-icon"></span>
        </button>
        <a class="navbar-brand" href="#">Brand</a>
        <div class="collapse navbar-collapse" id="navbar1">
            <ul class="navbar-nav">
                <li class="nav-item active">
                    <a class="nav-link" href="#">Link</a>
                </li>
            </ul>
        </div>
    </div>
</nav>

Bootstrap 3

Use navbar-fixed-top and then change the CSS to make it transparent. Here's an example of a custom transparent navbar. http://www.codeply.com/go/JNy8BtYSem

  <nav id="nav" class="navbar navbar-fixed-top" data-spy="affix">
    <div class="container">
        <div class="navbar-header">
      <a href="#" class="navbar-brand">Brand</a>
      <a class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">
        <i class="fa fa-bars"></i>
      </a>
      </div>
      <div class="navbar-collapse collapse">
        <ul class="nav navbar-nav">
          <li><a href="#">Link</a></li>
          <li><a href="#">Link</a></li>
        </ul>
        <ul class="nav pull-right navbar-nav">
          <li>
           <a href="#">Link</a>
          </li>
        </ul>
      </div>        
    </div>
  </nav>

This question is only to make the transparent Navbar. To change style after scrolling or at some Navbar position see: Animate/Shrink NavBar on scroll using Bootstrap 4