I've personally witnessed two types of Barks, and I know people like Elknut describe them differently even though the base sound is almost exactly the same.
Alarm Bark (Or whatever the hell you want to call it) - Several, many barks in succession as the Elk run away. Basically like a white tail blowing, flagging, and beating feet the hell out of town. Think of it as "RUN AWAY EVERYONE".
I've heard the other referred as the "Nervous Grunt", but to be honest I don't really care what it's called. The sound itself is exactly the same, but How it's been used towards me is a little bit more of a "Step out and show yourself..." I've had bulls do it to me without backing down and running away, but also not moving in any more, maybe 90-120 seconds apart as opposed to many in rapid succession. Basically - feel like they feel like they should have seen their challenger by now and want to see it visually.
The other time it was very clear to me was after I called a herd bull off of his herd of cows by imitating a dominant lead cow using lost / assembly mews - "Hey you, come here...". Well, the bull obliged and came in on a string down the hill mewing like a tabby cat, thinking he was going to get some. Wish I'd gotten a shot, but I needed one more step before he blew out and back up the hill. What happened next was that a pissed off dominant lead cow came down the hill and into view, and proceeded to "Bark" at me every 90-120 seconds for the next 10-20 minutes. Basically, looking for the "Cow" that was trying to steal her bull. I was pinned in place, so just froze and watched. She wasn't acting scared, but more like she wanted the offending cow to step out so she could smack it around...