There is no expanding bubble. The expansion of space means that the distance between all unbound objects increases over time. Stop and think about that for a moment. Any object without a sufficient attractive force will, over time, move away from you. If you instantly moved 1 billion light years away you will still see objects moving directly away from you, including the location you used to be at. After moving to this new location, you lose sight of some objects that you used to be able to see in your previous location (because you've moved and their light has not had time to reach your new location yet) but you will find that new objects have now been brought into your field of view. These new objects couldn't be seen in your previous location, again because their light hadn't had time to reach that location yet.
No matter where you go you will find the above holds true. Objects not bound to you will always be moving directly away from you and you will always find new objects entering your view as you move around the universe. This is, of course, only true if the universe is infinite in size. If not, then you may eventually come back around to your previous location (despite having moved directly away from it the whole time) or something else may happen. Current observations rule out a finite universe smaller than a certain size, with that size being some amount much larger than the observable universe. I confess I don't have a number for you.
Additionally, please note that the big bang did not occur at a single point in space. The singularity (if it ever actually existed) existed throughout the entire universe at the same time.