Applying Chosen after the modal is shown should solve your problem:
$('#myModal').on('shown.bs.modal', function () {
$('.chosen-select', this).chosen();
});
Or when Chosen was already applied, destroy and reapply:
$('#myModal').on('shown.bs.modal', function () {
$('.chosen-select', this).chosen('destroy').chosen();
});
Fiddle here: http://jsfiddle.net/koenpunt/W6dZV/
So in your case it would probably something like:
$('.someClick').click(function(e){
e.preventDefault();
x.modal('show');
x.on('shown.bs.modal', function(){
x.find('.modal-body').load('path/page.html', function(response, status, xhr){
if(status == "success"){
$("select[name=elementName]").chosen();
}
});
});
});
EDIT
To complement Chosen you can use the Chosen Bootstrap theme
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