The Bulls need to raise £1 million, half of it by 5pm on Friday, to stave off the threat of a winding-up petition and almost certain administration and have now reached another major landmark in pledges.
Bradford chief executive Ryan Duckett said: "The £300k figure is a significant milestone for the club to reach. We are delighted to have got that far and pledges are continuing to come in."
He added: "Pledges had slowed down earlier in the week but momentum has picked up again and we urge all supporters who haven't pledged to make sure they get them in before 5pm on Friday ahead of the Leeds game."
The Super League club also received support from BullBuilder, a supporters trust, following face-to-face talks with the Bradford board.
BullBuilder spokesman Mike Farren said: "As a result of the meeting, we are fully satisfied that the current situation has indeed arisen from the 'perfect storm' of adverse financial circumstances that the board has sought, we believe not always effectively, to explain.
"We are satisfied that, after the bank withdrew overdraft facilities, in the very short period available to it the board explored all other avenues before approaching the fans.
"Once they had concluded that only an approach to the fans could succeed in the tight time-frame, they went public as soon as they were commercially able to do so in a structured and organised manner.
"Should the club not receive the level of pledges and other support that is necessary, we are as sure as we can be that the board would have no alternative but to seek administration almost immediately. We remain of the view that this would be at best seriously detrimental, and at worst fatal, to top flight rugby league in Bradford.
"As a result, BullBuilder is supporting the Quest for Survival with a pledge of £2,500. We likewise urge those supporters who have so far been hesitant or reluctant to back the Quest for Survival to do so now, either via the pledge or other fund-raising activities."