Chris Hughton is a big fan of the midfielder, but his injury-prone history put the block on any permanent deal.
But Hughton could be interested in a season-long loan deal.
Hull's head of football operations Adam Pearson: "The deal is off as far as we are concerned - because of absolutely ridiculous financial demands being made by the player.
"We have bent over backwards to try to make this happen and four weeks ago there was an agreement with Celtic in place over a one-year loan.
"But now it seems Jimmy wants extra cash on top as well and he has jeopardised the chance to play for a great club. Who would not want to play at Celtic, with a chance of European football and silverware?
"Hull City were prepared to subsidise a year in Glasgow for Bullard. Let's just say we would have made a significant contribution to the overall wage package.
"But unless he has a dramatic change of heart overnight, we expect him back here rather than being in the United States with Celtic. He has had four weeks to make up his mind and has strung people along, frankly."