In a private listing, you can't see the userID of anyone else who bids. I believe that it also conceals the userID of the winner.
In theory this is so that no one besides you and the seller have to know about that embarrassing sex toy that you bought.
In practice this is a clever way for the seller to shill bid right up to your max, and there is nothing that you can do about it. I suppose that if that price is too low, the seller would probably "win" the auction, report non-payment to ebay, and re-list.
You don't have to avoid them entirely, but the final price will probably be the same as your max bid. Bid accordingly. If you get outbid, walk away.