I don't know a supported jQuery API function but I have this function:
var ret = data; // Your object
var childexpr = "b.b2"; // Your expression
if (childexpr != '') {
var childs = childexpr.split('.');
var i;
for (i = 0; i < childs.length && ret != undefined; i++) {
ret = ret[childs[i]];
}
}
return ret;