Again, this is where publishing the bidding comes into play.
If it's shown to the entire league that you're leading the bidding, and your offer keeps changing, people are going to know what you're doing. Maybe they pay anyway, maybe they back off and let you swallow the contract for a guy you didn't really want.
In real life, as I said, you always know who's in the running for a FA and for the most part, you know the current high offer. Why is it so secretive in HBD?
This whole issue aside, as I said earlier, if I know someone in my division is high bidder for a FA I don't particularly want, maybe I decide to go after him to keep him from that other team. If it's a team in the other league leading for him, I'll let him go.
Publishing the active bidders and highest bid could actually increase the competitiveness of the game. Could you drive up prices for guys you don't want? Sure. But you could also have your bluff called and be royally screwed with a contract you want no part of.