bootbox.confirm is asynchronus in behaviour so we can't stop its flow. we have to change our behaviour of the problem
first of all you have to prevent the default behaviour of bootbox by applying e.preventdefault(); then add your logic in true section whatever you want to do . then call server side function by using __doPostBack('btnDelete', 'OnClick');
$(function () {
$(".popup_button_delete").click(function (e) {
e.preventDefault();
var counter = GetSelected();
if (counter > 0) {
bootbox.confirm(' <%=GetLocalResourceObject("DeleteConfirm") %> ', function (confirmed) {
if (confirmed == true) {
__doPostBack('btnDelete', 'OnClick');
}
});
}
else {
bootbox.alert('<%=GetLocalResourceObject("NoSelectionAlert")%>');
}
});
});