You can use this SP WebService to do some of the work, the rest you'll have to use AJAX to do.
I'm not that strong in backend dev. but an example could be something like:
C#
public object JSONizedObject;
[WebMethod]
public static string GetWebAppPropertyBag()
{
// Logic goes here
JSONizedObject = new JavascriptSerializer.Serialize(PropertyBag object);
return JSONizedObject;
}
Javascript (jQuery)
<script type="text/javascript">
$.ajax({
url: "MyWebService.asmx/GetWebAppPropertyBag",
type: "POST",
contentType: "json/application; utf-8";
dataType: "jsonp"
success: function (xData, jqXHR) {
//Handle returned data here
},
error: function (jqXHR, responseType, responseText) {
//Error handling here
}
});
</script>
Hope this helps you :)