A couple of options:
If you only need to connect three or four wires besides power to the shield (look up what you're using and you might need to connect the reset) you could probably hard wire it from the top of the headers. You could also buy more expensive male-to-female jumper wires to put on the bottom, but you would have to flip it. (Keep it upside down)
You could buy both these from Sparkfun and normal headers OR this whole kit from Adafruit and put these in the breadboard and then set the shield on top of that. (The Sparkfun one is $1.25 for the only header you need modified and Adafruit for all of them should be $6). This article explains what they are and how to use them. Look under the
But wait... there's more header for how you will use this.
(Pretend the breadboard is the standard Arduino spaced clone and then you don't solder the board and you plug your shield on top of those adapters... read the link first and then this will make sense.)