click event to unhide something after ajax not firing

Your button was added dynamically. So you can not bind event in simple way.
As button is added after DOM is fully ready.

You need to bind it with the refrence of document or body

jQuery(document).on('click', '#readmore', function(e){
    e.preventDefault();
    alert("you clicked the button");
    jQuery("#bodytext").css("display", "block");
});

Read more about it here