<div class="container">
    <div class="page-header">
    <h1>Navbar with Full Screen Modal Search Form</h1>
  </div><!--  /page-header  -->
  
  <nav class="navbar navbar-default">
    <div class="container-fluid">
      <!-- Brand and toggle get grouped for better mobile display -->
      <div class="navbar-header">
        <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#bs-example-navbar-collapse-1" aria-expanded="false">
        <span class="sr-only">Toggle navigation</span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
      </button>
        <a class="navbar-brand" href="#">Brand</a>
      </div>

      <!-- Collect the nav links, forms, and other content for toggling -->
      <div class="collapse navbar-collapse" id="bs-example-navbar-collapse-1">
        <ul class="nav navbar-nav">
          <li class="active"><a href="#">Link <span class="sr-only">(current)</span></a></li>
          <li><a href="#">Link</a></li>
          <li class="dropdown">
            <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="false">Dropdown <span class="caret"></span></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 role="separator" class="divider"></li>
              <li><a href="#">Separated link</a></li>
              <li role="separator" class="divider"></li>
              <li><a href="#">One more separated link</a></li>
            </ul>
          </li>
        </ul>


        <ul class="nav navbar-nav navbar-right">
          <li><a href="#">Link</a></li>
          <li class="dropdown">
            <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="false">Dropdown <span class="caret"></span></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 role="separator" class="divider"></li>
              <li><a href="#">Separated link</a></li>
            </ul>
          </li>
          <li>


            <!-- Button trigger modal -->
            <button type="button" data-toggle="modal" data-target="#myModal" class="btn btn-default navbar-btn">
         <span class="glyphicon glyphicon-search" aria-hidden="true" ></span>
</button>

            <!-- Modal -->
            <div class="modal fade" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel">
              <div class="modal-dialog" role="document">
                <div class="modal-content">
                  <div class="modal-header">
                    <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">&times;</span></button>

                  </div>
                  <div class="modal-body">

                    <h1>Search</h1>
                    <form class="navbar-form " role="search">
                      <div class="form-group">
                        <input type="text" class="form-control" placeholder="Search">
                      </div>
                      <button type="submit" class="btn btn-default">Submit</button>
                    </form>


                  </div>


                </div>
              </div>
            </div>


          </li>
        </ul>
      </div>
      <!-- /.navbar-collapse -->
    </div>
    <!-- /.container-fluid -->
  </nav>

</div>
/* Jacob Lett - https//BootstrapCreative.com - Reference / Refresh / Repetition */

.modal-header {
  border-bottom: none;
}

.modal-dialog {
  width: 100%;
  height: 100%;
  margin: 0;
  padding: 0;
}

.modal-backdrop {
background-color:#fff;
  opacity:1!important;
    border: 10px solid rgba(136, 136, 136, .4);
}

.modal-content {
  height: auto;
  min-height: 100%;
  border-radius: 0;
  background: none;
  box-shadow: none;
}

.modal-body {
  text-align: center;
}

.modal-body form {
  margin: 0 auto;
  float: none;
  width: 300px;
}

.modal-content .close {
  opacity: 1;
  font-size: 30px;
}

.navbar-default .navbar-collapse,
.navbar-default .navbar-form {
  border: none;
}

External CSS

  1. https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css

External JavaScript

  1. https://cdnjs.cloudflare.com/ajax/libs/jquery/2.1.3/jquery.min.js
  2. https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/js/bootstrap.min.js