split and reduce while passing the object as the initalValue
var r = { a:1, b: {b1:11, b2: 99}};
var s = "b.b2";
var value = s.split('.').reduce(function(a, b) {
return a[b];
}, r);
console.log(value);
Update
(thanks to comment posted by TeChn4K)
With ES6 syntax, it is even shorter
var r = { a:1, b: {b1:11, b2: 99}};
var s = "b.b2";
var value = s.split('.').reduce((a, b) => a[b], r);
console.log(value);