U can use method "$(element).hasClass( string class )"
Example:
$('.bar-toggle').on('click',function(){
    if ($('.container').hasClass('.with_toggle')) {
       // mark as false 'cos in the next step u remove class .with_toggle
       localStorage.setItem("container_with_toggle", 0);
    } else {
       // mark as true 'cos in the next step u add class .with_toggle
       localStorage.setItem("container_with_toggle", 1);
    }
    $('.container').toggleClass('with_toggle');
});
When u access to localStorage:
var container_with_toggle = localStorage.getItem('container_with_toggle'); // return string zero or one ("0" or "1")
//So, u can use ternary
container_with_toggle = (container_with_toggle === "1") ? true : false;
And, if you set value like boolean localStorage.setItem("container_with_toggle", true), u can use ternary operator or JSON.parse.
var container_with_toggle = localStorage.getItem('container_with_toggle'); // return string with boolean notation ("false" or "true")
//Ternary
container_with_toggle = (container_with_toggle === "true") ? true : false;
// Or use JSON.parse
container_with_toggle = JSON.parse(container_with_toggle ); // return boolean true or false
Remember, in some browser u need use window.localStorage.
Bye!