Try specifying exactly the modal that the button should close with data-target. So your button should look like the following -
<button class="close" data-dismiss="modal" data-target="#myModal">×</button>
Also, you should only need bootstrap.modal.js so you can safely remove the others.
Edit: if this doesn't work then remove the visible-phone class and test it on your PC browser instead of the phone. This will show whether you are getting javascript errors or if its a compatibility issue for example.
Edit: Demo code
<html>
<head>
<title>Test</title>
<link href="/Content/bootstrap.min.css" rel="stylesheet" type="text/css" />
<script src="/Scripts/jquery-1.7.1.min.js" type="text/javascript"></script>
<script src="/Scripts/bootstrap.modal.js" type="text/javascript"></script>
<script type="text/javascript">
$(document).ready(function () {
if( navigator.userAgent.match(/Android/i)
|| navigator.userAgent.match(/webOS/i)
|| navigator.userAgent.match(/iPhone/i)
|| navigator.userAgent.match(/iPad/i)
|| navigator.userAgent.match(/iPod/i)
|| navigator.userAgent.match(/BlackBerry/i)
) {
$("#myModal").modal("show");
}
$("#myModalClose").click(function () {
$("#myModal").modal("hide");
});
});
</script>
</head>
<body>
<div class="modal hide" id="myModal">
<div class="modal-header">
<a class="close" id="myModalClose">×</a>
<h3>text introductory<br>want to navigate to...</h3>
</div>
<div class="modal-body">
<ul class="nav">
<li> ... list of links here </li>
</ul>
</div>
</div>
</body>
</html>