"Modal" commonly means a popup, when open other items on the page will be disabled. This is the behavior of bootstrap modal component, hence the name.
If you don't want this behavior, since you have jQuery UI available you can use it's dialog
component instead, which can be optionally made to behave like a modal if needed. The best part is that they are draggable and resizable by default.
Below is a simple demo using the same.
var $dialog = $('#dialog');
$dialog.dialog({
autoOpen: false
});
$('#open').on('click', function() {
$dialog.dialog('open');
});
<link href="//code.jquery.com/ui/1.11.4/themes/ui-lightness/jquery-ui.css" rel="stylesheet" />
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="//code.jquery.com/ui/1.11.4/jquery-ui.js"></script>
<div id="dialog" title="Basic dialog">
<p>This is the default dialog which is useful for displaying information. The dialog window can be moved, resized and closed with the 'x' icon.</p>
</div>
<button type="button" id="open">
1st click here then drag and resize the modal
</button>
<br>
<br>
<button type="button">Next I want to click here without close the modal</button>
For some reason if someone wants to use a bootstrap component over jQuery UI dialog (I can't think of a good reason) I think their closest bet is popover
component of bootstrap (Below demo has an issue with resizable, but should be fixable).
$('#open').popover({
html: true,
content: function() {
return $('#template').html();
},
placement: 'bottom'
}).on('inserted.bs.popover', function() {
$('.popover').draggable()
.resizable();
});
<link href="https://code.jquery.com/ui/1.11.3/themes/smoothness/jquery-ui.css" rel="stylesheet" />
<link href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css" rel="stylesheet" />
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="//code.jquery.com/ui/1.11.4/jquery-ui.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/js/bootstrap.min.js"></script>
<!-- Button trigger modal -->
<button type="button" class="btn btn-primary btn-lg" id="open">
1st click here then drag and resize the modal
</button>
<br>
<br>
<button type="button">Next I want to click here without close the modal</button>
<script type="text/tmplate" id="template">
<div class="" id="myModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" style="background-color: transparent;" data-backdrop="false" data-keyboard="false">
<div class="modal-dialog" role="document">
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span>
</button>
<h4 class="modal-title" id="myModalLabel">Notes</h4>
</div>
<div class="modal-body">
Sample text Sample text Sample text Sample text Sample text Sample text Sample text
</div>
</div>
</div>
</div>
</script>