Creating a post from data returned from HTML form

I worked it out and re-wrote the code:

jQuery(document).ready(function() {
    jQuery('#createacostume').submit(function( event ) {
        event.preventDefault();

        var aForm = jQuery(this);
        var bForm = aForm.serializeArray();
        bForm.push({name: 'action', value: 'myAjaxFunction'});
        jQuery.ajax({
            url: ajaxurl,
            type: "POST",
            data: bForm,

            success: function(resp) {

                alert("Thank you for your post. We will review it and approve it shortly" + resp);

            },
            error: function( req, status, err ) {
                alert( 'something went wrong, Status: ' + status + ' and error: ' + err );
            }
        })

                .fail(function() {
            alert("error");
        })
        ;
        return false;
    });
});

You have to push onto the form the ajax function you are calling.