What is this Private Bidder listing I see when checking bid status? How come they seem to always win and what does one do to earn this privilege status. That has always bugged me and nobody gives me a straight answer regarding it.

If you meant "Private Listing", that's when a seller decided to hide all bidders for whatever reasons.
It does not give any special privileges for buyer or seller, and has nothing to do with winning or losing.
You can find more information about it on the following link: http://pages.ebay.com/help/sell/private.html

If you meant "Private Feedback", that's just hiding your feedback from viewing by others. I honestly don't see any benefits of it except hiding a list of your purchased made in the past.
You can find more information about it here: http://pages.ebay.com/help/feedback/profile-public-private.html

Thanks for the speedy reply. I understand what you're saying and I am referring to the bidder's identity. It's funny because you can follow the bidding pattern by the time stamp. I still don't know how you make yourself anonymous though. Because even though ebay covers your identity to others, the fact remains that once you get to know a circle of people in certain interest areas, you can tell who it is because ebay only covers a few of the characters between the first and last character of userid names(i.e. ch******er,etc.)

eBay does not always use first and last characters. It also uses some characters in between as well, so you should not rely on being first and last only.
Anyway, when you see something like a***b, that's for all bidders. When others see you in the list, they see the same thing and not your actual eBay user id unless they try to guess it.

Thanks again for your response. It's a new experience getting such rapid response on a forum. Very refreshing and I thank you.