You have to handle the redirect in your Javascript. I hope the following will solve your problem:
$("#booking_form").validate({
debug: false,
submitHandler: function (form) {
// do other stuff for a valid form
$.ajax({
type: "POST",
url: '/booking',
data: $("#booking_form").serialize(),
dataType: "json",
success: function(data) {
if (data.redirect) {
// You can here redirect the user to the new page
window.location.href = data.redirect;
}
}
});
}
});