In fact, such an attack will make our situation "much, much, worse."
Shiite groups could be spending more time killing American troops. What's more, Iran could be giving such groups much better weapons than they have today. As I've pointed out before, just look at Hezbollah, whose weaponry is vastly more sophisticated than anything we've seen in Iraq. If we start bombing Iran, Iran has at its disposal cheap, effective means of retaliating against US forces in Iraq.
Bombing Iran in response to alleged Iranian meddling in Iraq won't help anything in Iraq in part, I think, because it isn't designed to. Rather, the Bush administration thinks it can't sell a second counterproliferation war against a Gulf country beginning with "Ira" because it's just too absurd. Hence, it would be nice to gin up a casus belli with Iran that's only tangentially related to the nuclear program. Not that bombing will help us with that problem either, but it's at least widely believed that it will. I don't think even the Bush administration is dumb enough to think that attacking Iran will help stabilize things in Iraq; the Iran-Iraq nexus is just a red herring designed to make it politically difficult to oppose what they're doing.