Hi there,
I bet this is a challenge many groups have faced. One thought is I would think the professional auctioneers would have some experience in handling this and perhaps you can ask them to offer suggestions.
But, a few other thoughts: You can make a few polite announcements at the start of and during the live auction (if necessary) for folks to be quiet during the bidding process. It may also help to create signs that say Quiet Please! Bidding Under Way! (make sure they are friendly signs!). You can have someone hold up the sign -- folks may respond to that.
Our school does an annual auction and one issue we have year after year is that some people like to continue chatting during the live auction. It's a very social group/event with alcohol so it's nice that people want to visit but when people talk during the live auction it prevents others from hearing/participating. We've hired professional auctioneers who also have difficulties navigating this. We will likely close the bar during the live auction but are there any other way/suggestions to respectfully ask people to keep the noise down just during this portion of the evening?