You can't "call a bean".
Backing beans are referenced when a JSF page request is made, and that requires an HTTP POST/response cycle. There's no short-circuit calling path - JSF is designed to present an entire formatted page (although certain add-ons like RichFaces can update parts of pages).
Setting up a JSF POST is not something that's easy (or safe) to do manually, so the better way of communicating with the bean is to write a custom
servlet that accesses the bean, and have the JavaScript function make an AJAX request to that servlet.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.