Remember Cardano is a public ledger, so anyone can read the values that are submitted to contracts.
It is possible to blind the data on a redeemer until after a deadline. You could have each submitted redeemer be hashed against a secret only known to the bidder. Once the deadline is passed, each bidder can choose to reveal their secrets, and thus their bids.
This still has a glaring problems though. The bid needs to also lock the funds for the bid (or else someone could just bid a billion ADA and never claim it). Each bidder would need to include more than their bid amount to be locked up, thus blinding the amount as well as giving some wiggle room for the next bidder. This seems less-than-ideal, since it still leaks information about their bid.
You'd need the bidders to lock their funds when they reveal their bid. This prevents a DoS from insincere bidders. Even then, you need to take into account that people might be incentivized to wait as long as possible to reveal their bids. This could create strange game theory.