|MadSci Network: Astronomy|
I think you have fallen prey to a fairly common misconception, which is that the Big Bang was some sort of explosion which occurred in space, or in the universe, resulting in matter and energy rushing out in all directions.
What actually happened, according to current theories of cosmology, is that at the moment of the Big Bang, the universe came into existence and was infinitely small. Space itself then expanded, growing into the universe that we see now. However, there wasn't a previously existing space inside which our own universe started.
For more information, you may want to look at Ned Wright's cosmology tutorial.
Try the links in the MadSci Library for more information on Astronomy.