Might have something to do with this as I have seen this on a few items for sale. IF YOU HAVE LESS THAN 5 POSITIVE FEEDBACK PLEASE CONTACT ME BEFORE YOU BID OR YOUR BID WILL BE REMOVED
I'm fairly sure that you can't tbh, as it was something I wanted to do a while ago as I buy and sell cars etc, sometimes on ebay and it's not helpful if you're trying to sell a car for 5k and the people bidding can see you only paid 2K last week. lol
I couldn't find a way to do it, it seems to hinge on whether the person whose listed the item has listed it as a private listing or a public one, that's when you get to see 'private' listed on your feedback, I don't think you can do it yourself.