I know that the decision was made to bomb Hiroshima in large part to put an end to the war but the need to intimidate Russia was part of it too. Why?
Being the only two remaining superpowers at the end of World War II, every other empire having been conquered or broke at that time, the post war period was one of jockeying for power and position.
The United States feared, rightly so, that the Soviet Union's goal was world expansion, and the exportation of revolution. So intimidation, especially where nuclear weapons were concerned, became an important and effective strategy for limiting Soviet expansion at that time. The Soviets didn't react very well to that intimidation, and the nuclear monopoly was short-lived, but it is understandable and predictable why the US reacted as it did.
I think the bombing of Hiroshima was in a sense more to do with sending a clear message to the USSR about American military might than it was about ending the war, to be honest. It was clear that the war was winding down. What was occurring was a jostling for positions the world over as powers sought to seize territory which they were able to do because of the instability of war. It was clear that ideologically the USSR and the USA were opposed, and thus there was the potential for conflict, which of course turned into the Cold War. It was a case of boys showing their toys to one another and seeing which ones were bigger.
I have to agree with the previous points that the Soviet Union was well on its way to being one of the world's superpowers, and they were obviously looking at expanding its borders further. I believe Truman may have realized that the two countries--the U.S. and USSR--would never line up as allies again, and he tried to exert the U.S.'s dominance over what he realized may one day be a worthy foe.
As mentioned in post number 4 I have never read or heard anything to suggest that the decision to use weapons of mass destruction had anything to do with sending Stalin a message. I would say however that the United States and Russia both felt it necessary to determine who the dominant country was after the end of the war.
I have read countless numbers of books, primary documents, reports, and declassified material concerning U.S. foreign policy, and I have never read anything to suggest that Truman's decision to drop the atomic bombs on Hiroshima and Nagasaki (like you say to end the war and ultimately save American lives) were to double as 'scare tactics' targeted at the Soviet Union. The failures at Yalta and Potsdam were becoming increasingly apparent by August 1945 to the U.S. and Britain. However, I think its fair to say that Truman and Churchill miscalculated and misjudged Stalin. Both men understood they were in for a long ideological fight with Stalin so to use the bomb as a 'bully pulpit' would only serve to heighten the already strained relations between them. The Library of Congress has a vast collection with regard to this subject. I've included it below.
I certainly think that you are on to something. I think that you can find a great deal of evidence to suggest that America wanted to send a message to Russia about its nuclear capacity. Certainly, Stalin was not someone that America trusted, having only allied with him through political and military expediency. The contentious discussions in peacetime settlements reflected the deep divide between both nations. The negotiations revealed that Stalin possessed a healthy distrust of America, almost as much as was felt towards him. The belief in the dropping of the bomb was that it would give America "the biggest stick on the playground," and could go very far in attempting to convince the Soviets that America was not to be dismissed as being able to back up its threats of global supremacy. Certainly, one cannot dismiss the diplomatic and political implications of dropping the atomic bomb.
In my opinion, the US felt the need to intimidate Russia because it was becoming clear that the USSR was going to try to be an expansionist power. Because the Soviets were going to try to expand their influence, many felt that it was necessary for us to flex our muscles to show them that they would not be able to just go wherever and do whatever they wanted.
It had become clear at the Potsdam Conference and the Yalta Conference that Stalin was going to try to get as much control over as much area as he could. Given that, it seemed necessary to sort of scare him -- to say "you better not try too much because we can do this to you too..."
You should also think about the fact that part of the reason for ending the war quickly was to prevent the USSR from gaining any more territory, especially in East Asia.