I was having the same problem but when I created a test project, to my surprise, datepicker worked perfectly using Bootstrap v2.0.2 and Jquery UI 1.8.11. Here are the scripts i'm including:
<link href="@Url.Content("~/Content/bootstrap.css")" rel="stylesheet" type="text/css" />
<link href="@Url.Content("~/Content/bootstrap-responsive.css")" rel="stylesheet" type="text/css" />
<link href="@Url.Content("~/Content/themes/base/jquery.ui.all.css")" rel="stylesheet" type="text/css" />
<script src="@Url.Content("~/Scripts/jquery-1.5.1.min.js")" type="text/javascript"></script>
<script src="@Url.Content("~/Scripts/jquery-ui-1.8.11.min.js")" type="text/javascript"></script>