Last week Cooper hinted that he would be prepared to quit the club if he cannot engineer a turnaround soon.
They have won just one of their last 10 League games, but Bullock insists the manager has the full support of his playing staff.
"It's up to the chairman and the board, but the players are 100 per cent behind the gaffer," Bullock told BBC Radio Kent.
"Everyone at the club has belief in the gaffer - I came here because I'd worked with Neale Cooper before, and I hope that he's staying in the job.
"Once the injured players come back, our fortunes could change."