You will need to make use of jQuery and call Validations using JavaScript.
HTML
<link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/css/bootstrap.min.css" />
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.9.1/jquery.min.js"></script>
<script type="text/javascript" src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.2/js/bootstrap.min.js"></script>
<div class="panel panel-default" style="width: 500px; padding: 10px; margin: 10px">
<div id="Tabs" role="tabpanel">
<!-- Nav tabs -->
<ul class="nav nav-tabs" role="tablist">
<li><a href="#personal" role="tab" >Personal
</a></li>
<li><a href="#employment" role="tab" >Employment</a></li>
</ul>
<!-- Tab panes -->
<div class="tab-content" style="padding-top: 20px">
<div role="tabpanel" class="tab-pane active" id="personal">
<div class="form-group">
Name:
<asp:TextBox ID="txtName" runat="server" CssClass="form-control" Width="150" placeholder="Enter name" />
<asp:RequiredFieldValidator ID="RequiredFieldValidator1" ErrorMessage="Required" ControlToValidate="txtName" runat="server"
ForeColor="Red" />
</div>
</div>
<div role="tabpanel" class="tab-pane" id="employment">
This is Employment Information Tab
</div>
</div>
</div>
<asp:Button ID="Button1" Text="Submit" runat="server" CssClass="btn btn-primary" />
<asp:HiddenField ID="TabName" runat="server" />
</div>
<script type="text/javascript">
$(function () {
var tabName = "personal";
$('#Tabs a[href="#' + tabName + '"]').tab('show');
$("#Tabs a").click(function () {
$('#Tabs a[href="#personal"]').tab('show');
tabName = $(this).attr("href").replace("#", "");
if (Page_ClientValidate()) {
$('#Tabs a[href="#' + tabName + '"]').tab('show');
}
});
});
</script>
Screenshot
