One reason for a bounty office not to reveal who placed the bounty is the same reason that Lokrin kept people who put bounties though him anonymous. Anonymity is good for the business. Keep the placers of bounties secret, and more people should place them.

But if you don't like the idea of secret bounties, then I submit that the idea of allowing someone to pay more than the bounty just to find out who placed it is a good one.