Colchester registered 22 goal attempts but could find no way past Ricketts.
The Jamaican international had spent most of this season on the bench but showed that he is a keeper with terrific potential.
Colchester dominated the first half and Ricketts was in the action early on as he saved Richard Garcia's goalbound header.
Ricketts was in the right place to smother an eight-yard shot from Neil Danns on the half-hour mark and he then denied Ryan Jarvis and midfielder Gavin Johnson with smart saves in quick succession.
Bradford were poor in the first half with home keeper Aidan Davison not having a serious save to make but they did improve after the break.
Leading scorer Dean Windass should have been celebrating but he sent a free header wide of the target following Marc Bridge-Wilkinson's 62nd minute corner.
Davison then made some late saves to thwart Ben Muirhead and substitute Danny Forrest, while fellow substitute Lewis Emanuel blew a great opportunity to snatch victory for the Yorkshire side by blasting wide in stoppage time.