Don't miss this.

<nav class="navbar navbar-default navbar-fixed-top" role="navigation">
    <div class="container">
        <!-- Brand and toggle get grouped for better mobile display -->
        <div class="navbar-header">
            <button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#bs-example-navbar-collapse-1">
                <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</a></li>
                <li><a href="#">Link</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><a href="#">Separated link</a></li>
                        <li 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">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><a href="#">Separated link</a></li>
                    </ul>
                </li>
            </ul>

            <form class="navbar-form" role="search">
                <div class="input-group">
                    <input type="text" class="form-control pull-right" style="width: 300px; margin-right: 35px, border: 1px solid black; background-color: #e5e5e5;" placeholder="Search">
                    <span class="input-group-btn">
                        <button type="reset" class="btn btn-default">
                            <span class="glyphicon glyphicon-remove">
                                <span class="sr-only">Close</span>
                            </span>
                        </button>
                        <button type="submit" class="btn btn-default">
                            <span class="glyphicon glyphicon-search">
                                <span class="sr-only">Search</span>
                            </span>
                        </button>
                    </span>
                </div>
            </form>
        </div><!-- /.navbar-collapse -->
    </div><!-- /.container-fluid -->
</nav>

In addition, it includes CSS styles

    body {
    padding: 60px 0px;
}
.navbar-collapse {
    position: relative;
    padding-top: 30px !important;
    max-height: 270px;
}
.navbar-collapse form[role="search"] {
    position: absolute;
    top: 0px;
    right: 0px;
    width: 100%;
    padding: 0px;
    margin: 0px;
    z-index: 0;
}
.navbar-collapse form[role="search"] button,
.navbar-collapse form[role="search"] input {
    padding: 8px 12px;
    border-radius: 0px;
    border-width: 0px;
    color: rgb(119, 119, 119);
    background-color: rgb(248, 248, 248);
    border-color: rgb(231, 231, 231);
    box-shadow: none;
    outline: none;
}
.navbar-collapse form[role="search"] input {
    padding: 16px 12px;
    font-size: 14pt;
    font-style: italic;
    color: rgb(160, 160, 160);
    box-shadow: none;
}
.navbar-collapse form[role="search"] button[type="reset"] {
    display: none;
}

@media (min-width: 768px) {
    .navbar-collapse {
        padding-top: 0px !important;
        padding-right: 38px !important;
    }
    .navbar-collapse form[role="search"] {
        width: 38px;
    }
    .navbar-collapse form[role="search"] button,
    .navbar-collapse form[role="search"] input {
        padding: 15px 12px;
    }
    .navbar-collapse form[role="search"] input {
        padding: 25px 12px;
        font-size: 18pt;
        opacity: 0;
        display: none;
    }
    .navbar-collapse form[role="search"].active {
        width: 100%;
    }
    .navbar-collapse form[role="search"].active button,
    .navbar-collapse form[role="search"].active input {
        display: table-cell;
        opacity: 1;
    }
    .navbar-collapse form[role="search"].active input {
        width: 100%;
    }
}

Additionally, there is a small JS file included

    $(function () {
    // Remove Search if user Resets Form or hits Escape!
    $('body, .navbar-collapse form[role="search"] button[type="reset"]').on('click keyup', function(event) {
        console.log(event.currentTarget);
        if (event.which == 27 && $('.navbar-collapse form[role="search"]').hasClass('active') ||
            $(event.currentTarget).attr('type') == 'reset') {
            closeSearch();
        }
    });

    function closeSearch() {
        var $form = $('.navbar-collapse form[role="search"].active')
        $form.find('input').val('');
        $form.removeClass('active');
    }

    // Show Search if form is not active // event.preventDefault() is important, this prevents the form from submitting
    $(document).on('click', '.navbar-collapse form[role="search"]:not(.active) button[type="submit"]', function(event) {
        event.preventDefault();
        var $form = $(this).closest('form'),
            $input = $form.find('input');
        $form.addClass('active');
        $input.focus();

    });
    // ONLY FOR DEMO // Please use $('form').submit(function(event)) to track from submission
    // if your form is ajax remember to call `closeSearch()` to close the search container
    $(document).on('click', '.navbar-collapse form[role="search"].active button[type="submit"]', function(event) {
        event.preventDefault();
        var $form = $(this).closest('form'),
            $input = $form.find('input');
        $('#showSearchTerm').text($input.val());
        closeSearch()
    });
});