If you want to achieve this result all you have to do is to do the folowing (full code here):
First you need to use bootstrap accordion and set it fixed to bottom. After this you must style it like the one from your example. I did all of this with this css code:
#accordion {
    position: fixed;
    bottom: 0;
    width: 100%;    
}
.panel-default > .panel-heading{
    background: #00B4FF;
}
.panel-heading {
    padding: 0;
    border-top-left-radius: 0px;
    border-top-right-radius: 0px;
}
.panel-group .panel {
    border-radius: 0;
}
.panel-title a {
    color: #FFFFFF;
    text-align: center;
    width: 100%;
    display: block;
    padding: 10px 15px;
    font-size: 24px;
    font-family: Helvetica,Arial,sans-serif;
    outline: none;
}
.panel-title a:hover, .panel-title a:focus, .panel-title a:active {
    text-decoration: none;
    outline: none;
} 
The bootstrap accordion html code looks like this:
<div class="panel-group" id="accordion">
    <div class="panel panel-default">
        <div class="panel-heading">
            <h4 class="panel-title">
                <a data-toggle="collapse" data-parent="#accordion" href="#collapseOne">
                    Click Me
                </a>
            </h4>
        </div>
        <div id="collapseOne" class="panel-collapse collapse">
            <div class="panel-body">
                Lorem ipsum dolor sit amet, consectetur adipisicing elit. Voluptatibus, adipisci, quibusdam, minima ratione voluptas quidem porro sint nobis odio cupiditate alias nisi. Magnam et fugiat labore eum at adipisci ex.
            </div>
        </div>
    </div>
</div>
And if you want to achieve the background color change effect, you should use the accordion events in javascript like this:
$('#collapseOne').on('show.bs.collapse', function () {    
    $('.panel-heading').animate({
        backgroundColor: "#515151"
    }, 500);   
})
$('#collapseOne').on('hide.bs.collapse', function () {    
    $('.panel-heading').animate({
        backgroundColor: "#00B4FF"
    }, 500);   
})
You will need to load Jquery UI for this background color change and in case you want to optimize your code take a look at this question.
Anyways, you have the full code here in jsfiddle.