You can always negotiate at the gate; just turn down their offer. "I bid $500 thinking I could take another flight that arrived only two hours later, but you're offering me one that arrives 4 hours later so I want $800." If they say they'll find someone else who'll take $500, let them. Maybe they will, but you don't want to VDB for that so you lost the auction.

At check-in, when bidding, I seldom accept an amount they suggest, I type in my own (higher, of course).