No country will stand by and allow itself to be bombed, especially one that has closer ties with the Shiite Iraqi people than the American Christians do. Your assumption is that it would only be a bombing, Iran would surely respond by boming the green zone with Missiles and through its tremendous influence and support within Iraq proper. It would also attack in Afghanistan. Any dreams of a stable (democratic) regime in Baghdad would be gone, the straits would be surely closed by Iran, which could very easily escalate into a ground offensive. The people who say this can be done are the same people who have been wrong in EVERY prediction about Iraq. The pourus border with Afghanistan and Iraq would increase 100 fold the transfering of arms to insurgents in both countries. The Shiitte would surely side with Iran, and it would spiral way out of control, costing a painful blow to the US in tax money, military lives (possibly a draft) and hardware. While Russia and China rise to power.
U.S. says working on initiative to de-escalate Syria fighting, with focus on Aleppo (Reuters)
from the article: U.S. army chief: Iraq war has sapped ability to fight Iran