ebay make all bidders confidential by keeping the full ID private to everyone except the seller and the Buyer.

All bidders on an item will see other bidders ID as a**2 or some other mix of letters or numbers.

Private listings are usually used for high end items such as Jewellery or Coins or for Personal items which  the Buyer may wish to keep private.

A Private listing only keeps the item private plus marks the bidders as Private Bidders rather than a**2.

Try clicking on the Add/Remove option above the Auction /Fixed Price box. Hopefully it should come up then.