Found the answer myself :-)
I added an if exists statement to the beginning to check for the cookie, and also added managed to discover where to add the {expires: 1} parameter to the slideToggle code purely by chance.
$(document).ready(function(){
if($.cookie('billboardStatus')) {
var cook = $.cookie('billboardStatus');
} else {
var cook = $.cookie('billboardStatus', 'true', {expires: 1});
}
//var cook= $.cookie('billboardStatus');
if(cook=='false') {
$('#billboard').hide();
$("#billboardButton").css("backgroundColor", "#e1e1e1").text('Open Ad');
} else {
$('#billboard').show();
$("#billboardButton").text('Close Ad');
}
$('#billboardButton').on('click', function() {
$('#billboard').stop().slideToggle('normal', function(){
$("#billboardButton").css("backgroundColor", $(this).is(':not(:visible)') ? "#e1e1e1" : "").text($(this).is(':visible') ? 'Close Ad' : 'Open Ad');
$.cookie('billboardStatus', $(this).is(':visible'), {expires:1});
});
});
}); // End document ready