What is preventing your desired results is that you are iterating over the class' __bases__ - these only list the immediate superclasses. If you change your metacass to iterate over __mro__, Python's linearized sequence of all of one class' ancestors, it will work:
In [14]: class Abstract(metaclass=Meta): 
    ...:     def __call__(self): 
    ...:         print("Abstract") 
    ...:  
    ...: class Base(Abstract): 
    ...:     def __call__(self): 
    ...:         print("Base") 
    ...:  
    ...: class Super(Abstract): 
    ...:     def __call__(self): 
    ...:         print("Super") 
    ...:  
    ...: class Parent: 
    ...:     def __call__(self): 
    ...:         print("Parent") 
    ...:  
    ...: class Child(Parent): 
    ...:     def __call__(self): 
    ...:         print("Child") 
    ...:                                                                                                            
In [15]: Child.__mro__                                                                                              
Out[15]: (__main__.Child, __main__.Parent, object)
Anyway, this turns out to be a bit trickier than seem at first glance - there are corner cases  - what if one of your eligible classes do not feature a  __call__ for example? What if one of the methods do include  an ordinary "super()" call? Ok, add a marker to avoid unwanted re-entrancy in cases one does put a "super()" - what if it is running in a multithreaded environment and two instances are being
creaed at the same time?
All in all, one has to make the correct combination of using Python's attribute
fetching mechanisms  - to pick the methods in the correct instances. I made a choice of copying the original __call__ method to anothr method in the class itself, so it can not only store the original method, but also work as a marker for the eligible classes.  
Also, note that this works just the same for __call__ as it would work for any other method - so I factored the name "__call__" to a constant to ensure that (and it could be made a list of methods, or all methods whose name have a certain prefix, and so on).
from functools import wraps
from threading import local as threading_local  
MARKER_METHOD = "_auto_super_original"
AUTO_SUPER = "__call__"
class Meta(type):
    def __new__(meta, name, bases, attr):
        original_call = attr.pop(AUTO_SUPER, None)
        avoid_rentrancy = threading_local()
        avoid_rentrancy.running = False
        @wraps(original_call)
        def recursive_call(self, *args, _wrap_call_mro=None, **kwargs):
            if getattr(avoid_rentrancy, "running", False):
                return
            avoid_rentrancy.running = True
            mro = _wrap_call_mro or self.__class__.__mro__
            try:
                for index, supercls in enumerate(mro[1:], 1):
                    if MARKER_METHOD in supercls.__dict__:
                        supercls.__call__(self, *args, _wrap_call_mro=mro[index:], **kwargs)
                        break
                getattr(mro[0], MARKER_METHOD)(self, *args, **kwargs)    
            finally:
                avoid_rentrancy.running = False
        if original_call:
            attr[MARKER_METHOD] = original_call
            attr[AUTO_SUPER] = recursive_call
        return super().__new__(
            meta, name, bases, attr
        )
ANd this is working on the console - I added a few more
intermediate classes to cover for the corner-cases:
class Abstract(metaclass=Meta):
    def __call__(self):
        print("Abstract")
class Base1(Abstract):
    def __call__(self):
        print("Base1")
class Base2(Abstract):
    def __call__(self):
        print("Base2")
class Super(Base1):
    def __call__(self):
        print("Super")
class NonColaborativeParent():
    def __call__(self):
        print("Parent")
class ForgotAndCalledSuper(Super):
    def __call__(self):
        super().__call__()
        print("Forgot and called super")
class NoCallParent(Super):
    pass
class Child(NoCallParent, ForgotAndCalledSuper, Parent, Base2):
    def __call__(self):
        print("Child")
Result:
In [96]: Child()()                                                                                                  
Abstract
Base2
Base1
Super
Child
Forgot and called super
Child