It's not so much a direct relationship between helicopters and strategic bombing as it is a much more subtle influence in tactics that have developed since. In fact, if you want to go back further still you can draw a line from modern helicopter tactics to cavalry tactics and infer a relationship from these as well. Where most other nations of the time utilized cavalry formations as a massed shock unit, civil war cavalry generals are known for employing their units in a manner that closely relembles the basic employment of helicopter formations on the modern battlefield. Of course I am in no way attempting to equate the two on an even plane, but rather pointing out an interesting relationship between the two.
As for the development of the helicopter by the US into a tank killer, in the US you must really go back to the Vietnam war. Actually, let me take you back first to 1948 and the key west agreement. This agreement attempted to define the respective service roles of the branches. This agreement, among some others, basically relagated the helicopter to the mission of observation and evacuation. Any type of armed air role, including helicopters fell into the purview of the USAF. The Air Force, however, was rather uninterested in the use of the helicopter as an offensive weapon. Which is why the United States waited untill the Vietnam War to begin arming it's helicopters. There are several instances in fact of Army officers advocating the use of the helicopter as a gun platform in the Korean war but there was reluctance to be seen as violating the percieved service roles and perhaps losing the new Army aviation to the Air Force.
Now the Vietnam war saw the first major use by the US of the helicopter in an offensive role, and ushered in the United States' first dedicated attack helicopter the AH1. This all dovetails nicely with the advent of precision munitions at the end of the conflict. Shortly thereafter you have helicopter carrying the first guided anti tank weapons such as the TOW for the US and the role of the helicopter as a dedicated tank buster began in earnest.