Updated 2018
Do you want to close the modal after submit? Whether the form in inside the modal or external to it you should be able to use jQuery ajax to submit the form.
Here is an example with the form inside the modal:
<a href="#myModal" role="button" class="btn" data-toggle="modal">Launch demo modal</a>
<div id="myModal" class="modal hide fade" tabindex="-1" role="dialog" aria-labelledby="myModalLabel" aria-hidden="true">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal" aria-hidden="true">×</button>
<h3 id="myModalLabel">Modal header</h3>
</div>
<div class="modal-body">
<form id="myForm" method="post">
<input type="hidden" value="hello" id="myField">
<button id="myFormSubmit" type="submit">Submit</button>
</form>
</div>
<div class="modal-footer">
<button class="btn" data-dismiss="modal" aria-hidden="true">Close</button>
<button class="btn btn-primary">Save changes</button>
</div>
</div>
And the jQuery ajax to get the form fields and submit it..
$('#myFormSubmit').click(function(e){
e.preventDefault();
alert($('#myField').val());
/*
$.post('http://path/to/post',
$('#myForm').serialize(),
function(data, status, xhr){
// do something here with response;
});
*/
});