I came here by mistake, but having had a look at the answers, and seen that many people are looking for it, I have posted this answer.
There is, in fact, an easy way to do all that.
You can use the bootstrap native classes 'visible-xs' and 'hidden-xs', this will automatically hide or show one of the two controls depending with which device the users are opening the page.
An example is given here:
<div class="tabbable">
<ul class="mb10 nav nav-pills nav-justified form-tabs hidden-xs">
<li class="tab-selector active"><a href="#tab1" data-toggle="tab">Tab 1</a></li>
<li class="tab-selector"><a href="#tab2" data-toggle="tab">Tab 2</a></li>
<li class="tab-selector"><a href="#tab3" data-toggle="tab">Tab 3</a></li>
<li class="tab-selector"><a href="#tab4" data-toggle="tab">Tab 4</a></li>
<li class="tab-selector"><a href="#tab5" data-toggle="tab">Tab 5</a></li>
</ul>
<select class="mb10 form-control visible-xs" id="tab_selector">
<option value="0">Tab 1</option>
<option value="1">Tab 2</option>
<option value="2">Tab 3</option>
<option value="3">Tab 4</option>
<option value="4">Tab 5</option>
</select>
<div class="tab-content">
<div class="tab-pane active" id="tab1">
Content tab 1
</div>
<div class="tab-pane" id="tab2">
Content tab 2
</div>
<div class="tab-pane" id="tab3">
Content tab 3
</div>
<div class="tab-pane" id="tab4">
Content tab 4
</div>
<div class="tab-pane" id="tab5">
Content tab 5
</div>
</div>
</div>
Place this javascript snippet in the document ready function" and put it at the end of </body>
tag and well in the </body>
tag and NOT outside of it. Of course you must have jQuery up and running.
$(document).ready(function() {
$('#tab_selector').on('change', function (e) {
$('.form-tabs li a').eq($(this).val()).tab('show');
});
});
A working demo can be found here: https://jsfiddle.net/fr0w59n9/