invalid use of non-static data member

In C++, unlike (say) Java, an instance of a nested class doesn’t intrinsically belong to any instance of the enclosing class. So bar::getA doesn’t have any specific instance of foo whose a it can be returning. I’m guessing that what you want is something like:

    class bar {
      private:
        foo * const owner;
      public:
        bar(foo & owner) : owner(&owner) { }
        int getA() {return owner->a;}
    };

But even for this you may have to make some changes, because in versions of C++ before C++11, unlike (again, say) Java, a nested class has no special access to its enclosing class, so it can’t see the protected member a. This will depend on your compiler version. (Hat-tip to Ken Wayne VanderLinde for pointing out that C++11 has changed this.)