Jenny, have you ever read
Talking to Dragons? The wizard staffs in that are exactly as you describe. (I love that series by the way.

)
I'm glad my analogy could be helpful, so here's another. Think of a light bulb. Alone, in and of itself, it cannot create light. It requires electricity, Electricity, on the other hand, needs the light bulb to make it useable. However, when you suddenly throw 400 watts through a 60 watt bulb,
it explodes. That's what I think happened to Gandalf's staff on the Bridge. The massive power surge Gandalf used on the bridge overwhelmed the conduit.
Saruman's staff exploding can be explained in the same way. Gandalf merely sent a massive power surge through the staff, causing it to break. He just sent the surge through a different conduit. Like lightening striking a different lightening rod.
EDIT:As for why Saruman was weakened and not powerless after this, he lacked the ability to focus his power into a useful force. Going back to the light energy analogy, it's the difference between flourescent light bulbs and a laser beam.