My horse did the same thing - nipped at the air in my general direction, one time, each time I buckled up the girth. I just figured she didn't like it being tightened. She seemed fine once it was tight and I was on.
Eventually, as she got older and her back sagged more, it was apparent that the saddle didn't quite fit right. She was old, I wasn't riding much, so I just got a 1" foam pad to go under the saddle.
She never nipped again after the first ride with that pad.
Now from what I've read on threads here, this behavior is often - probably usually - behavioral, but in my case it clearly related to discomfort from the saddle, which had been going on for years and I hadn't caught. Hey, the saddle looked like it fit, sweat patterns were even, etc!