I think the bulls start to get antsy in mid-August and throw some bugles off on occasion.
I was in Yellowstone NP the first week of June many years ago and witnessed an elk tragedy. A cow elk was standing belly deep in a small stream while her calf was struggling to climb out of the water.
I had to pull over and run back to watch things unfold, and as I got there, the calf lost it's grip and started to slowly spin in the water, trying to keep it's head above water, and all the while, the cow is frantically running into and out of the water, bugling like crazy. After many bugles from her, I heard a bugle from another group of elk a few hundred yards away. No chuckles at the end, just straight whistling/bugling.
Up until that time, I had no idea that cow's were capable of bugling.